For a birth in 1822 you need to rely on church baptism records, where they exist. (And they are probably not on-line). You don’t say what denomination Andrew was. Portglenone Church of Ireland lost its early records in the 1922 fire and has none before 1873. Portglenone 1st Presbyterian has no records before 1826, 2nd start in 1821 & 3rd in 1869. RC records start in 1864. So only 1 church in the parish has any records for 1822. The 2nd closed in about 1912 but a copy of their records is in PRONI in Belfast. (Personal visit required to view them).
If Andrew was Protestant and married 1845 onwards in Ireland, you should get his father’s name from the marriage certificate.
There were about 12 Mooney farms in the Portglenone area in 1834. See the tithes here: