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. Without a KNOWN county, there is AT LEAST a 35% chance your ancestor's rcds aren't in this database.
For Cec(ily) Gallen, the only 2 B rcds I found that fit your timeline are both in 1898 Tyrone. One had a father's name of John, the other Thomas.
B/M/D registration was civil after 1863. Civil rcds are at the General Register Office. Contact this office at http://www.groireland.iehttp://www.groireland.ie.
Google the Foundation's name to lead you to this database. Pls post your search results to my genforum msg.