I research 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.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For Mary O'Loughlin B 1830 +/- 4 yrs in Co. Sligo with the father forenamed Mich(ael), I found 5 B rcds: 1831, 3-1832, and 1833.
For Michael O'Loughlin (+variants) in Co. Sligo, I found 1 M in 1832, Sligo parish.
For Mary Royan (+variants) in Co. Sligo, I found 0 M rcds in Sligo parish.
The M rcds are a NO MATCH. M rcds in Sligo parish don't start until 1831. The B rcd for Mary O'Loughlin MAY be in those identified above. A view of the detailed rcds SHOULD show BOTH parent names. This fact will validate/invalidate a rcd.
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.