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. Unless you KNOW the county of origin, the chance that your ancestors' rcds AREN'T in the database is AT LEAST 35%.
For the surname Mulvihill in Ballinameen in Co. Roscommon, I found 0 B and 0 M rcds at any date. There are Mulvihills in Co. Roscommon, just not in this parish. Try to find some forenames.
B/M/D registration was civil after 1863 and comprehensive. Civil rcds are kept at the General Register Office. Contact it at http://www.groireland.iehttp://www.groireland.ie for certificate copies. Fees apply.
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.