Basically my challenge, if you accept it, is to have a Fascist Ireland with any POD after the Easter Rising. Bonus points if you have said Fascist Ireland join the Axis.
The best candidate is Eoin O'Duffy and the Irish Blue Shirts to come to power. This could happen in a few situations, I was personally toying with the idea of a much larger Easter Rising along with the Germans arms arriving too. This would give enough difference to really change things enough where a Blue Shirt takeover of Ireland is much more likely.
The odds are low, and even if it happened, they'd likely be neutral out of fear of the British(which they'd use anti-British propaganda).