One ofthe main issues you're going to run into is that the Confederates ended up falling in with the royalist faction, believing that their goals (and to anti-Catholic laws, greater self government, the roll back of the plantations and so forth) would be better met under James and and the Stuarts. Because of this - even if they are always going to be viewed by the Parliamentarian factions as a knife poised directly at the heart of the government. A surviving Confederation is going to become a beacon to royalists from across Britain, and likely those who come to chaff under the Lord Protector. Also, should a Glorious Revolution still occur, the changes arethat Ireland would be rolled back into joint rule along with England and Scotland.
What you are going to need is one of two things:
1) The Confederates reach out to the Parliamentary forces and form an alliance with them - Parliament agrees to the establishment of an independent Irish state (NOT under the role ofthe Stuarts) should they win the conflict. This will be tricky, especially as religious differences mean that the English Republic is always going to view Ireland would suspicion, even if they start as allies - it will be very hard for any such Irish state to not fall into the orbit of another Catholic power (read: France or Spain) and that could prove a very existential threat to the Parliamentary government.
2) Stop the Confederates from entering into such a close alliance with the royalists - the agreement caused a split within the Confederates which made it difficult if not impossible for them to respend effectively to the Parliamentary invasion in 1649. You might have the Confederates do better in turning back the Scottish Conventary invasions, and make the Confederate position in Ireland more secure. However, in this case, the Confederates' best bet is still likely eventually drift further into the Royalist camp, and that is going to bring the inevitable dissention within their own ranks, and bring up the problems in
2b) (okay, I'm cheating on the numbering here). The Confederates manage to get a general who is as capable of Cromwell and pull together a fighting force that is more than a match of the New Model Army (which will be difficult, considering the poliitcal makeup of Confederate Ireland, but we'll leave that discussion for another time). They win a stronger string of victories than in OTL, drive the Conventors back into Scotland and smash them there. They then turn around and are able to fight Cromwell to a standstill (preferably not on Irish soil). The Confederates are associated with the Royalist cause, but not so closely tied that a royalist defeat spells their doom. Licking his wounds, Cromwell turns his attention back to England and Scotland - he's too weak to invade Ireland again, but conversely the Confederation is too weak to launch a counter invasion and do something crazy like put Charles on the throne. A stalemate eventually develops - especially after France offers its support.
I suppose there is also option 3) The Confederates throw their lot in with the royalists, who win. However, James feels as if he can't go back on his agreement and agrees to the Confederate demands. You get an end to Anti-Catholic laws and a rolling back of the plantations, and the Kingdom of Ireland is ruled by James but remains largely independent of England, with its own parliament, foreign policy and the like. James really, really, really, hates this - but, well, he needs one Kingdom that is assuredly loyal, so he's willing to bite the bullet.
So, the issue really is: in all of these situations (except the last one) Ireland's position remains very precarious and will always be viewed with suspicion, at best, by England and will likely be viewed a an existential threat that needs to be taken care of. Ireland's best bet is to try to move into the French or Spanish orbit in such a case - but that move would just confirm the fevered nightmares of any British parliamentarian. And in the last situation: the entire scheme rests of James' good will and ability to keep agreements with a parliament - and the entire Civil War would have likely been avoided if James was able to do these things in the first place.
