Government of Ireland Bill of 1886 is passed. IOTL it lost 341-311 so change the mind of 16 Liberals who voted against their government and job done.
Except this doesn't solve the internal issues that plagued Ireland or the serious split in the Liberal Party the Bill engendered that would undermine any lasting settlement.
What you actually need here is an attitude shift among Irish Protestants (particularly in Ulster) that prevents them from seeing Home Rule as Catholic Domination. Without this they will derail the Dominion almost immediately (they were ready to fight the British Govt for the right to be "British" in 1914 remember).
One POD that could work would be for a more widespread growth of Protestantism in the rest of Ireland, maybe in reaction to the Land Wars of the 1870s and 1880s. Instead of being hounded out as absentee landlords, maybe Protestant owners decide to play a more active and supportive role towards their catholic tenants, thus eases tensions in time for the 1886 Bill to pass.
A more realistic settlement would be post 1900, for Asquith to hold his nerve and push Home Rule through in 1914-1915 when the nation was distracted by the war. This would give the new Dominion four years of unifying conflict to start to ease into its new identity.