Ballymoney Church of Ireland has baptisms, marriages and burials from 1807 onwards. There is a copy in PRONI in Belfast. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
You can also write to the Rector of the church and ask if he will search them for you. He doesn’t have to do that, but if he does there is normally a fee. When I last checked it was £19 (sterling) an hour plus there can be additional costs depending on precisely what you want. Some churches are more accommodating than others. Many get a lot of requests for genealogical assistance and don’t have the time to respond. The shorter the work involved generally the more likely a positive response. If you are looking for a specific baptism on a given date, then that’s fairly easy but if you are look for all the Smiths in the records since 1807, then they won’t normally do that.
Rev AJ Sweeney
4 Queen Street
The Church of Ireland does have a project running to put all it’s surviving records on the irishgenealogy site. However Covid has stopped that work and it will be some years before the project is complete. Your best option, if you can’t get to PRONI yourself is perhaps to hire a researcher. PRONI is closed at present but will re-open when it’s safe to do so.
Rev Park compiled a census of everyone in Ballymoney parish in 1817. That’s available on Bill Macfee’s website: http://billmacafee.com You might find it helpful if you get back that far.