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 Michael Hoban B 1870 +/- 1 yr, Dunmore CP, Co. Galway, with a father forenamed Michael, I found 1 rcd in 1870.
For Michael Hoban M 1866 +/- 4 yrs, Dumore CP, Co. Galway, I found 1 rcd in 1865.
For Mary McGragh M ditto, I found ditto. This and Michael's M rcd are likely for these ancestors. A view of the detailed rcd should show the marriage was to each other. If so, this validates the rcds. Usually, the M rcd will also show their parents' names. These facts will help you identify the couple's birth rcds if they exist.
Note B rcds before 1864 were kept by churches. There is no church parish named Dunmore. The birth rcds for these individuals, if they exist, will appear under a different name. It likely won't be Tuam because Tuam is in Galway west while all my other findings were in Galway east.
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.