This is very early for records for Armagh
The Tithe Applotment is the only surviving record used as a census substitute. These are the only Reilly/OReilly's listed for Armagh.www.genealogy.nationalarchives.ie
Oreilly James, Parish Shrule, Townland Ledwithstown
Oreilly John, Parish Shrule, Townland Drynan
Reilly James, Parish Shrule, Townland Doonacurry
Reilly John, Parish Shrule, Townland Drynan
John is the most popular of Irish names with James just behind. Usually first son if not named after Henry he would be named after Henry's father. So a good guess would be John.
By the time of the Griffith Valuation (census substitute)
in 1864 the Parish of Shrule is not listed so probably has been amalgamated into another parish. Would need to look up the history.
Now there are 81 Reilly's occupying land, many nameswww.askaboutireland.ie
The only Shrule is in the Tithe's, however, beside that is
in brackets and bold Armagh.
Back to an Irish History Foundation with baptism records
Parish Armagh has birth records RC from 1796-1900 marriages 1802-1810, 1816-18223, 1835-1900
Parish of Armagh, Cof I baptism records from 1801-1822, marriages same
There are two sources for baptism and marriages for Northern Ireland:www.emeraldancestors.com
free to view pay for a recordwww.rootsireland.ie
pay website but not for profit Foundation.