Just back from N Ireland ourselves, having taken own car from Edinburgh and Cairnryan -Belfast ferry: not cheap or quick, just convenient having our own car! Daughter and family say flying over and hiring a car is cheaper: they go quite often. They now favour Easyjet to Belfast International, which, although further out of the city, is more reliable than Flybe to Belfast City: too many times they were delayed with the latter.
The Citylink buses say Edinburgh to Belfast: ferries all go from Cairnryan now, so don't think Stranraer comes into it, but will check!
Do make time for a day at the Titanic exhibition: it took us 4 hours to go round, then there's also the SS Nomadic included in same ticket!