We could call them both Eyre (Papist) and Eyre (Damned) and annoy everyone even more thoroughly, although I sincerely doubt anything will work in the opposite direction and calm the situation. Someone said at the beginning of this that this is one of those longstanding disagreements; I concur it will not be easily or even perhaps ever resolved. Take it back to the 'pedia, via talk pages and dispute resolution, as whatever happens on this list it cannot by definition resolve any content dispute on wiki.
One puppy's opinion.
Andrew Gray wrote:
Maybe we should compromise on calling the country [[Secessionist Ireland]], and rename [[Northern Ireland]] to [[Occupied Ireland]]. Annoy and mislead both sides equally :-)
More seriously, what I don't understand here is why there's opposition to primary disambiguation at [[Ireland]], at least as a temporary measure - I get the impression there's not any broad support for the current approach as the best option, and almost everyone seems to concur "Republic of Ireland" isn't very good. You seem to be the one with experience of the fight...