A small part of the 1821 census for Co Fermanagh has survived and there is 1 James McCort in it of about the right age. Whether it is your James I have no way of knowing without more information:
http://www.census.nationalarchives.ie/pages/1821/Fermanagh/Derryvullan/Druminchinmore/6/
You really need James parents names from a marriage or death certificate to be certain of finding the right family. If James was Protestant then, in Fermanagh, he was probably Church of Ireland. Not all Church of Ireland records for Fermanagh go back to the early 1800s. Some were lost in the 1922 fire in Dublin. In addition not all those that have survived are on-line. The most complete collection for Fermanagh is in PRONI (the public record office) in Belfast. However a personal visit is required to access them.