www.rootsireland.ie/ has Blackwatertown Parish records but they are Civil so start in 1864 I'm afraid.
There are records for Moy - county Tyrone Diocese Armagh but he's not there.
Do you know his religion?
I checked the RCBL's C of I parish lists and there are no tecords for Blackwatertown but there are for Moy: births 1625 to 1880; marriages 1826 to 45 and Burials 1826 to 1880. However if you're in the states you'll need to get someone to look them up for you unless you visit of course.
If R C the National Library has the parish records freely available at registers.nli.ie/ Nothing for Blackwatertown but a search for Moy brings up Clonfeacle and there are baptisms & marriages from 1814 to 1881