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).
I couldn't find a Henry Tully - Mary Metcalf marriage in this Irish database. Quite possible he married in England. The Metcalf surname is rare in Ireland, but the Tully name is abt 12 times more prevalent and therefore, Irish. I think Henry was born in Ireland and migrated to England to escape the Famine.
For Henry Tully B 1841 +/- 4 yrs somewhere in Ireland with an unknown father's forename, I found 1 B rcd in 1838 Galway. This is a long shot. Suggest you investigate Henry and Mary's history in England via the censuses.
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.