I've discovered from British Military records that my 4th great-grandfather, Edward Courtney, was born in Glenavy, Antrim around the year 1780. If anyone has any info about Courtneys in Glenavy, please post a note. Thanks.
You don’t say what denomination your Courtney ancestor was. Looking at the 1901 census for Glenavy, there were 3 households, all in Aghadolgan townland. 2 were RC and 1 was Church of Ireland.
The RC parish records only start in 1849 but the Church of Ireland records go back to 1707, so that might be promising.
In addition there was a census taken in 1826 of the whole parish. It’s in the Church of Ireland records but should include all denominations. The Church of Ireland records have been copied and are held in PRONI (the public record office) in Belfast. A personal visit is required to view them.