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 John Hughes B 1835 +/- 4 yrs in Armagh, I found 32 B rcds.
For Mary Murray B 1837 +/- 4 yrs in all Ireland, I found 421 B rcds. This assumes she was born in Ireland. This number is impossibly large. Suggest you research Canadian M and or census rcds to find an exact DOB, placname, and/or parents names. You will need something to eliminate the false positives.
Google the Foundation's name to lead you to this database. Pls post your search results to this genforum msg.