Irish Neutrality
Some inaccuracies in some of these postings, I'm afraid. The Eire Government DID present condolences to the German Ambassador in Dublin on May 1st 1945, an action roundly condemned by the British Government and different to the attitude of the Swedes, who did not present condolences.
I think perhaps Hitler might have offered Eire Ulster in the event of the defeat of Britain but the end of British control of Ulster as well as Gibraltar would have been the inevitable consequence of British defeat.
It's not generally known that Dublin was bombed on a number of occasions by the Germans in 1940 and 1941. The German pilots thought the city was Liverpool which, without radar and in the dark, I suppose is understandable.
As others have argued, Irish neutrality was far from even-handed and the same was true of Swedish neutrality. From 1940-42, the onus was on not antagonising the Germans - from then on, it became a question of co-existing with the allies.
I'm puzzled as to why Ireland didn't join the war on the Allied side in say March 1945, along with the likes of Egypt and Turkey. I suppose it would have been a gesture but, as others have commented, amny thousands of Southern Irishmen volunteered and fought for the allies.
Had Ireland voluntarily joined the Axis, say in June 1940, it might have been very difficult for the British if German forces had been able to operate out of Dublin, Cork and Rosslare and German aircraft would have been able to bomb more effectively. That said, I'm also sure that in the light of the Norway experience, the British would have moved first even with their weakened post-Dunkirk forces and occupied key Irish centres before the Germans.