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 Francis O'Shaughnessy B ???? in Galway with the father's forename unknown, I found 3 rcds in Galway east: 2-1866, and 1874. Galway west: 1863 and 1866.
For Mary Gorman B ???? in Galway west: 1862, 1865, 1867, 1871, 2-1876, 3-1880, & 1885. Galway east 1862, 2-1871, 1872, 2-1873, 1874, 1875, 1878, 1879, 2-1882, and 1884.
Since there are a lot of rcds, suggest you search Boston civil and church rcds for their marriage. These rcds should identify their parents' names. This knowledge would reduce the number of false positives enormously.
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.