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 Marg(aret) McDaid M 1897 +/- 4 yrs, Co. Donegal, I found 6 rcds: 1893, 2-1894, 1897, 1898 Malin CR, and 1901 Malin CR.
For Charles Mooney M ditto, I found 5 rcds: 3-1898 (1 in Malin CR), and 2-1901. The Malin CR rcds are highly likely to be for your ancestors. A view of them will show if they married each other. If so, the view will also give the correct parents' names as well as other info.
For Marg(aret) McDaid B 1876, Carndonagh district, Co. Donegal, with the father's forename unknown, I found 1 rcd. Father's forename was Dan(iel).
For Dan(iel) McDaid M 1872 +/- 4 yrs, Co. Donegal, I found 11 rcds: 1868 Churchill CR, 1868 Movil CR, 1870 Raphoe CR, 1871 Carndonagh CR, 1871 Ramelton CR, 1872 Movil CR, 1873 Cloghan CR, 1874 Raphoe CR, 1875 Ramelton CR, 1875, and 1876 Malin CR. I couldn't find a corresponding marriage rcd for Ellen in these yr/parish combinations.
For Ellen Callaghan M ditto, I found 15 rcds: 2-1868, 1870, 1871 Churchill CR, 1871, 3-1872, 2-1873, 1874, 1875, 1876, 1876, 1876 Cloghan CR.
For Daniel McDaid B 1847 +/- 4 yrs, I found 0 rcds.
Will leave it to you to search for the children's DOB.
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.