It depends on the POD.
One possible way to get this would be a British defeat in World War I, or even World War II, but that has huge implications beyond Ireland.
Another way is that the Tories don't side with the Ulster Protestants in the home rule debate, or institute home rule itself. Note that if the British avoid attempting to introduce conscription to Ireland, the island becomes an autonomous part of the British empire, but not independent. And this requires a pre 1900 POD.
It was actually the formation of the Republic of Ireland that was produced by an improbable chain of events, because the Ulster protestants would not agree to be governed by a parliament elected by a majority Catholic electorate, and at least the Conservative Party in Britain backed them. And its hard to see the Conservatives not backing them given the importance of Ulster to the British military establishment (as a source of recruits for the army and the shipyards for the navy), which in turn was linked to the Conservatives.
Another possibility is the leaders of the Ulster Protestants themselves negotiate joining the republic, which is also difficult to pull off, but in this scenario the climate in the republic would be favorable to the orangemen. Note that the OTL Irish republic has had Protestant presidents.