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 county, 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 Peter Scully B 1890 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 5 rcds: 1888 Dublin, 1889 Tipperary, 1889 Tyrone, 1889 Longford, and 1891 Roscommon. Father's forenames were Joseph, Patrick, Peter, Peter, and William.
Lally is also an Irish surname, but there are NO Anitas in this database. Perhaps she used Anita rather than Agnes.
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.