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 Marg(aret) Mullarkey B 1895 +/- 4 yrs, Co. Sligo, with a father forenamed Patrick, I found 2 rcds: 1895 and 1897. The respective parishes were Cloonacool and Kilmacteigue.
For Pat(rick) Mullarkey M 1881 +/- 4 yrs in Co. Sligo, I found 1 rcd in 1881, Cloonacool RC parish.
For Marg(aret) McGoldrick M ditto, I found 3 rcds: 1878, 1881 and 1885. The 1881 rcd is also in Cloonacool RC parish. This and Patrick's rcd are highly likely to be for your ancestors. A view of the detailed rcd SHOULD show the marriage was to each other. If so, then they will likely list their parents' names and other info. This will help you validate their B rcds below.
For Marg(aret) McGoldrick B 1860 +/- 4 yrs in Co. Sligo with the father's forename unknown, I found 3 rcds: 1856, 1857, and 1863. Father's forenames were "An," James, and James respectively. Parishes are all the same: Kilmacteigue.
For Pat(rick) Mullarkey B 1858 ditto, I found 6 rcds: 1855, 2-1859, 3-1861. Five were in Kilmacteigue parish.
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.