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 Mary Harley B 1799 +/- 4 yrs in Co. Armagh, I found 0 rcds. For all Ireland using the same range, I found 0 B rcds.
For John Henry B 1795 ditto, ditto. For all Ireland ditto, I found 6 B rcds: 1794 Louth, 1795 Meath, 1796 Louth, 1796 Westmeath, 1796 Meath, and 1798 Meath.
Assuming they married in Ireland, for Mary Harley M 1822 +/- 4 yrs, I found 0 rcds in both Armagh and all Ireland. Without at least 1 rcd for Mary, it makes no sense to search for Henry. They MAY have married in CN. Suggest you search the censuses to find ages and a place, then go to the oldest RC church in that area and search the parish registers.
Google the Foundation's name to lead you to this database. Pls post your search results to this genforum msg.