This is a very, very rough timeline, so please forgive me if I make a bunch of mistakes ....
c. 1585 Oda Nobunaga unifies Japan under his rule and survives for many years. He forges strong links with Portuguese and Spanish representatives. The Japanese begin to copy European techniques for making heavy cannon and fortifications, as well as the muskets that they have already learned to make well.
1581 - King Philip of Spain becomes King of Portugal
1588 - Spanish Armada defeated, plans for Spanish to invade England fail.
1591 - 1598 - Japanese invasion and conquest of Korea. Naval defeats by Korean forces spur Japanese to build stronger, better armed ships, at least partly modeled after Spanish galleons. The Koreans continue guerrilla resistance with Chinese support for years to come.
c1600 - Growing internal unrest and military defeats against Japan and others prod the Ming government into attempting some tentative reforms that did not happen in OTL.
1603 - England and Scotland both come under the rule of King James of the Stuart dynasty.
1607 - In North America, the French settle at Quebec and the English at Jamestown
1609 - Oda Nobunaga dies. His son and successor maintains control of Japan and further strengthens ties with the Spanish and Portuguese.
1612 - The Oda ruler assumes the formal title of Shogun. All trade with Europeans other than the Spanish and Portuguese is forbidden.
Japanese are encouraged to settle in Korea as the last major guerrilla resistance is wiped up.
1618 - "Defenestration of Prague" marks the beginning of the 30 Years' War in Europe.
1620 - English Separatists, a strongly Calvinist religious group, settle at Plymouth, Massachusetts Bay in North America.
1624 - 1628 - China is racked by civil war. A prominent general, distantly related to the ruling family, raises a revolt against the Emperor and the corrupt eunuchs who are widely regarded as the greatest obstacle to reform. Large sections of the army and peasantry rally to this generals' standard. In 1627, rebel forces capture Beijing. The new Emperor is actually from a family offshoot of the ruling Ming family, so he keeps the title for his dynasty. Historians will generally refer to this new dynasty as the "Later Ming".
1630-33 - Chinese Emperor defeats Manchu and Mongol forces who had seized Chinese territory during the civil war.
1642 - Beginning of English Civil War between supporters of the King and supporters of Parliament.
1648 - End of 30 Years' War in Europe. Spain's power is greatly reduced, while France has become much more powerful. The Netherlands are formally recognized as independent from Spain after decades of de facto independence.
1649 - Charles I, formerly King of England and Scotland, is beheaded. Parliament takes control of England.
1650 - First Emperor of "Later Ming" dynasty dies. His son is determined to eliminate the last vestiges of resistance to the new dynasty.
1651 - The ruler of Taiwan, a loyalist to the old Ming dynasty, signs an agreement with the Shogunate of Japan in which the Japanese will help defend the island against any attempt to capture it from mainland China in return for major trade and political concessions that basically make the island a protectorate of Japan.
1656 - Chinese attempt to invade Taiwan is crushed by superior Japanese naval forces. The Chinese are shocked and soon begin to take a stronger interest in the large-scale use of modern gunpowder weapons.
1660 - Stuart dynasty is restored to power in England and Scotland.
1670s and 1680s - King Louis XIV of France fights a series of wars against the Dutch, Austrians, Spanish, and several other enemies. France gains a little more territory, the gains are not decisive.
1680s - Tsar Alexei II takes the throne is Russia, and begins a program to modernize Russia's armies. (Butterflies mean that Peter the Great is never born, and instead we have Alexei II, who is also interested in reform. He is considerably more cautious and less daring than Peter the Great in OTL, but he is also much less autocratic and brutal toward opposition.)
1680s - China expands trade with Dutch and English merchants. Techniques for building cannon, muskets, and ships are borrowed and modified by the Chinese.
1688 - King James II of England, who has converted to Catholicism, announces that now he has a son and heir to the throne. Many of the Protestant elite are appalled, and plot to bring in his Protestant daughter Mary, along with her Dutch husband William, as the new rulers. William crosses to England with a substantial army. James panicks at first, but later rallies some of his forces.
1689 - 1693 - Second English Civil War James suffers a series of defeats, first in England and Wales and then in Ireland. Eventually, he and many of his supporters flee to France. During this fighting English, Dutch, and Scottish Protestant leaders manage to form a strong working relationship. Mary has a son in 1693, who is also named William (although there are whispered doubts about his true parentage.)
1695 - The Japanese shogunate dissolves the puppet government on Thailand and declares the island a province of Japan itself.
1704 - King Charles II of Spain dies childless. There had long been controversy over the issue of whether the French Bourbons or the Austrian Hapsburgs would get to inherit the Spanish throne. In the end, Charles leaves the throne to the Bourbon candidate, Louis' nephew Philip. Austria, England, and the Netherlands will not accept this.
1704 - 1712 - War of the Spanish Succession - In spite of some setbacks, this war is generally favorable to France. (One possible reason is that Marlborough, who played an important role in the war in OTL, was killed in the 2nd English Civil War in this timeline.) When the war ends, the Bourbons are confirmed as the ruling dynasty of Spain, with the future possibility of unification of the French and Spanish thrones. France gains considerable territory at the expense of Savoy and the Spanish Netherlands (which are compensated with a little piece of Dutch territory. Overseas, French Acadia is seized by the British, but Canada remains in French hands. The British get Minorca, but fail to take Gibraltar.
1706 - William dies, his son becomes King William IV of England and Scotland, and Stadtholder of the Netherlands.
1707 - China invades the lightly-defended Spanish Phillippines.
Here is a map of what I expect this world to look like in another 100 years or so -
c. 1585 Oda Nobunaga unifies Japan under his rule and survives for many years. He forges strong links with Portuguese and Spanish representatives. The Japanese begin to copy European techniques for making heavy cannon and fortifications, as well as the muskets that they have already learned to make well.
1581 - King Philip of Spain becomes King of Portugal
1588 - Spanish Armada defeated, plans for Spanish to invade England fail.
1591 - 1598 - Japanese invasion and conquest of Korea. Naval defeats by Korean forces spur Japanese to build stronger, better armed ships, at least partly modeled after Spanish galleons. The Koreans continue guerrilla resistance with Chinese support for years to come.
c1600 - Growing internal unrest and military defeats against Japan and others prod the Ming government into attempting some tentative reforms that did not happen in OTL.
1603 - England and Scotland both come under the rule of King James of the Stuart dynasty.
1607 - In North America, the French settle at Quebec and the English at Jamestown
1609 - Oda Nobunaga dies. His son and successor maintains control of Japan and further strengthens ties with the Spanish and Portuguese.
1612 - The Oda ruler assumes the formal title of Shogun. All trade with Europeans other than the Spanish and Portuguese is forbidden.
Japanese are encouraged to settle in Korea as the last major guerrilla resistance is wiped up.
1618 - "Defenestration of Prague" marks the beginning of the 30 Years' War in Europe.
1620 - English Separatists, a strongly Calvinist religious group, settle at Plymouth, Massachusetts Bay in North America.
1624 - 1628 - China is racked by civil war. A prominent general, distantly related to the ruling family, raises a revolt against the Emperor and the corrupt eunuchs who are widely regarded as the greatest obstacle to reform. Large sections of the army and peasantry rally to this generals' standard. In 1627, rebel forces capture Beijing. The new Emperor is actually from a family offshoot of the ruling Ming family, so he keeps the title for his dynasty. Historians will generally refer to this new dynasty as the "Later Ming".
1630-33 - Chinese Emperor defeats Manchu and Mongol forces who had seized Chinese territory during the civil war.
1642 - Beginning of English Civil War between supporters of the King and supporters of Parliament.
1648 - End of 30 Years' War in Europe. Spain's power is greatly reduced, while France has become much more powerful. The Netherlands are formally recognized as independent from Spain after decades of de facto independence.
1649 - Charles I, formerly King of England and Scotland, is beheaded. Parliament takes control of England.
1650 - First Emperor of "Later Ming" dynasty dies. His son is determined to eliminate the last vestiges of resistance to the new dynasty.
1651 - The ruler of Taiwan, a loyalist to the old Ming dynasty, signs an agreement with the Shogunate of Japan in which the Japanese will help defend the island against any attempt to capture it from mainland China in return for major trade and political concessions that basically make the island a protectorate of Japan.
1656 - Chinese attempt to invade Taiwan is crushed by superior Japanese naval forces. The Chinese are shocked and soon begin to take a stronger interest in the large-scale use of modern gunpowder weapons.
1660 - Stuart dynasty is restored to power in England and Scotland.
1670s and 1680s - King Louis XIV of France fights a series of wars against the Dutch, Austrians, Spanish, and several other enemies. France gains a little more territory, the gains are not decisive.
1680s - Tsar Alexei II takes the throne is Russia, and begins a program to modernize Russia's armies. (Butterflies mean that Peter the Great is never born, and instead we have Alexei II, who is also interested in reform. He is considerably more cautious and less daring than Peter the Great in OTL, but he is also much less autocratic and brutal toward opposition.)
1680s - China expands trade with Dutch and English merchants. Techniques for building cannon, muskets, and ships are borrowed and modified by the Chinese.
1688 - King James II of England, who has converted to Catholicism, announces that now he has a son and heir to the throne. Many of the Protestant elite are appalled, and plot to bring in his Protestant daughter Mary, along with her Dutch husband William, as the new rulers. William crosses to England with a substantial army. James panicks at first, but later rallies some of his forces.
1689 - 1693 - Second English Civil War James suffers a series of defeats, first in England and Wales and then in Ireland. Eventually, he and many of his supporters flee to France. During this fighting English, Dutch, and Scottish Protestant leaders manage to form a strong working relationship. Mary has a son in 1693, who is also named William (although there are whispered doubts about his true parentage.)
1695 - The Japanese shogunate dissolves the puppet government on Thailand and declares the island a province of Japan itself.
1704 - King Charles II of Spain dies childless. There had long been controversy over the issue of whether the French Bourbons or the Austrian Hapsburgs would get to inherit the Spanish throne. In the end, Charles leaves the throne to the Bourbon candidate, Louis' nephew Philip. Austria, England, and the Netherlands will not accept this.
1704 - 1712 - War of the Spanish Succession - In spite of some setbacks, this war is generally favorable to France. (One possible reason is that Marlborough, who played an important role in the war in OTL, was killed in the 2nd English Civil War in this timeline.) When the war ends, the Bourbons are confirmed as the ruling dynasty of Spain, with the future possibility of unification of the French and Spanish thrones. France gains considerable territory at the expense of Savoy and the Spanish Netherlands (which are compensated with a little piece of Dutch territory. Overseas, French Acadia is seized by the British, but Canada remains in French hands. The British get Minorca, but fail to take Gibraltar.
1706 - William dies, his son becomes King William IV of England and Scotland, and Stadtholder of the Netherlands.
1707 - China invades the lightly-defended Spanish Phillippines.
Here is a map of what I expect this world to look like in another 100 years or so -