Considering that Nortern Ireland is a money drain, with inhabitants represented by two bunches of intolerant bigots, when would had been the best moment to dump it? Making it into a dominion?
I believe I have read somewhere that around 1960 some Prot politicos were making such noises themselves, taking offence over London wringing its hands over them lording over disenfranchised Kafflicks.
Maybe later 70s/early 80s?
The best option might have been some sort of deal on self-government in ~1914. I did read once that during Redmond's attempts to get Home Rule for Ireland he had the agreements of the northern Unionists given some concessions to assure them they wouldn't get totally side-lined but that one of the smaller Catholic parties objected to the concessions and Redmond wanted to try and keep everybody on board.
If that had gone differently then you might have seen a unified Ireland by peaceful means, quite possibly staying inside a wider UK. It would have faced problems from extremists from both sides, bit especially the 'Catholic' extremists given the hard-liners would have wanted to suppress them totally and also cut any links with Britain but hopefully that could be overcome.
Even the OTL coup attempt in 1916 was initially bitterly rejected by the bulk of the southern population and could have itself been a turning point in draining some of the poison there. Unfortunately, although probably understandably given the world war ongoing at the time and that the extremists had openly proclaim their support of Germany and the aid they had received from it, London allowed the local military to try the guilty in military rather than civilian courts which did a lot to alienate people.
I do remember sometime in the 1970's IIRC there was talk of an independent Ulster state, which it was alleged would get support from both factions - although I find that hard to believe given the level of hatred and mistrust, as well as the vested interests of the extremists on both sides. However don't think it was ever anything serious.
