I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
For James Johnson B 1815 +/- 4 yrs in Armagh, I found 4 B rcds: 1811, 1815, 1817, & 1818.
For Cath(erine) Kearney there are only 3 B rcds in Armagh within a relevant range of yrs: 1800, 1807, and 1829. None of these look feasible. In all Ireland, there are 36 B rcds.
For a Catherine and James marriage in Armagh in 1839 +/- 4 yrs, there are 0 B rcds for Catherine. Searching all Ireland, there are 32 M rcds. For James, there are 19 M rcds in all Ireland. The only common year and county are 1840 Westmeath. Will leave it to you to screen to see if the marriages occurred in the same Westmeath parish.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.