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 George Farney B ???? somewhere in Ireland with the father's forename unknown, I found 0 rcds at anydate, anywhere. The surname Farney doesn't seem native to Ireland. There are only 32 B rcds for it. Could be Scotch.
For Mary Guinan B ditto, I found 191 rcds with 5 for a Mary Ann: 1861 Roscommon, 1870 Limerick, 1871 Limerick, 1890 Galway, and 1890 Roscommon. Note - for most of the 19th century it was no common to record a middle name even if the individual had one.
For immigration rcds after 1891, google ellisisland. For rcds before 1892, google castlegarden.
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.