I research the Irish Family History Foundation's database. It contains 12,800,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Cos. Donegal and Derry were recently added to the database.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 30%.
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 Rose Gorry M ????, somewhere in Ireland, I found 1 rcd in 1861, Co. Westmeath, Mullingar RC parish.
For Martin McInerney M 1861, Co. Westmeath, I found ditto. These are highly likely to be for these ancestors. A view of the detailed rcd should confirm the marriage was to each other. If so, the view should reveal their parents' names as well as other details.
For Marg(aret) McInerney B 1878 +/- 4 yrs, somewhere in Ireland, with a father forenamed Martin, I found 0 rcds. I did find an 1876 B rcd in Westmeath, Castletown-Geoghan RC parish, but the father's forename in the database is Matthew. There is only a slim chance that this is for your ancestor. A view of the detailed rcd should reveal whether the mother's name is correct.
For "E" McInerney B ???? ditto, I found an Elizabeth in 1878, Castletown-Geoghan RC parish with a father forenamed Martin. Again, this is a slim chance.
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.