Gibson, I’m looking for records from what is now Northern Ireland, perhaps County Down

1846Galway,

Statutory recording of births didn’t start in Ireland till 1864. Prior to that we rely on church baptism records, where they exist. Not all churches have records for the period you need, and of those that do, not all are on-line. Copies are held in PRONI (the public record office) in Belfast but a personal visit is required to view them. But without some idea of where in NI the family lived, it's a needle in a haystack.

I note that the family were Free Presbyterians. Probably a third of the population were Presbyterians. Cooper and Gibson are very common names locally. Thousands of them. That makes it hard too. I have attached a link to the Rosdavies Co Down site. You’ll see how many John & Mary Gibsons there were in that county alone.

https://freepages.rootsweb.com/~rosdavies/genealogy/SURNAMES/G/GibsonAJ.htm

Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. If you have already tested your DNA with Ancestry, My Heritage or 23&Me you can upload your DNA results to Family Tree DNA for free and then join the North of Ireland Family History Society DNA Project. Simple instructions on how to do this can be found here:

https://www.nifhs.org/dna/uploading-your-dna/