Thank you both for being so helpful. The tithe applotments are particularly useful, for the fact that no Paisley is shown (and as a farmer, I would expect James to be) suggests that perhaps the Paisleys came into the parish from somewhere else after about 1830. This is one more piece of evidence which points me towards Newtownards, particularly the Ballyblack Paisleys, who were also farmers ad who feature on Beattie's Newtownards website (I wish the sources were given!) The names David and James crop up there several times. It's not been sitting right with me that my David is described as a hosier, which I would associate more with Newtownards than with Drumhirk. I also know that David was brought out to Durham in England by the Marquis of Londonderry, after he married the heiress to many of the Durham coal pits, and I have read that Londonderry relocated some of his tenants to the Durham pits during the famine. So it would make more sense that David was living in Newtownards and was a tenant of Londonderry, rather than Drumhirk, where Lord Dufferin was the main landowner. David's marriage certificate states "father unknown" whereas Agnes' father is named as John Gamble, labourer, so I think the registrar would have recorded David's father had he known it. There is a Susanna Paisley who married a Drumhirk man, John Whitlaw or Whitla, and had two daughters by him in 1834 and 1841. I am now speculating that she was perhaps originally married to William Paisley, the gun license holder, that he died when David was only about 10, so David didn't know his name. Perhaps Susanna was dead by the time of David's marriage in 1846 so she couldn't tell him. I note that David' second daughter is named Susanna, and third daughter Agnes, suggesting they used the traditional naming pattern. In addition, some of the Ballyblack Paisleys emigrated to Pittsburgh, and David's son Hugh also gave this a try in 1880, also to Pittsburgh. This is the scenario I am going to work with, I think.
I see that the graveyard site says that all the pre-1865 Kilmood gravestones have been copied. Do either of you know where I could get a list of these? I'd like to see if it includes James 1837. I have also been told that the early Ballyblack Paisleys might be associated with the Millisle Presbyterian church, so I need to try and track those registers down. Unfortunately, they are not on Familysearch (Killinchy is, but there is no sign of any Paisleys.) I think Millisle and 1st Presbyterian Newtownards might be my best bet now.
Once again, thank you very much for your help. I'm an experienced genealogist, but in England, not Northern Ireland, where I am a complete beginner, so all help is gratefully received.
Carolyn