You say you are uncertain of Arthur’s father’s name. That information should be on the 1851 marriage certificate. If you haven’t got a copy, you can view it on the GRONI site for £2.50. According to the rootsireland site (which has transcripts) his name was David and he was a labourer. Margaret’s father was James, a farmer.
The Clarke family should be easier to research because they evidently were settled in Clontonakelly and their baptisms etc should be in the Presbyterian records for that area which I have detailed in my previous post. But you’ll need to get someone to go to PRONI to do that as they aren’t on-line so far as I am aware. If you think the Fullertons also came from that area, then I would search the same records. But I note that David Fullerton was a labourer. They tended to move about a bit, so can be hard to trace.
Clontonakelly is not really Belfast. It’s an agricultural area now on the outskirts of the city but which in the 1850s was a rural area some miles from the city. You have said Arthur and Margaret came from Belfast but I suspect Margaret at least came from Clontonakelly and that’s not Belfast. I mention that because it is important to identify which church records to search. There are over 50 Presbyterian churches in Belfast. No point searching those if they didn’t actually live there.
Couple of probate abstracts, presumably relating to Margaret’s father:
Administration of the estate of James Clarke late of Clontnacally County Down Farmer who died 25 December 1885 granted at Belfast to James Clarke of Clontnacally Farmer the Son.
And perhaps to another relation:
Clarke James of Clontonakelly Carryduff county Down farmer died 12 November 1935 Probate Belfast 14 April to William Frederick McNeill farmer. Effects £4 3s. 6d.
