You haven’t said what denomination your McCourt family was. If Churhc of Ireland their records start in 1692. If RC they start in 1815. So if RC you may struggle to get back any further. If Churhc of Ireland, then there is scope for researching further back. Some years are on the rootsireland site (subscription) but they don’t have all the records. There is a full set in PRONI (the public record office) in Belfast. If they were some other denomination, let me know and I’ll see what the nearest church may have been.
It’s Ireland Reaching Our policy not to give out details of living people so I am not able to advise whether there are any McCourts in the area today.