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 Mic(hael) Cryan B 1874 +/- 2 yrs, Co. Leitrim, with a father forenamed John, I found 2 rcds in 1874: 1-Civil, 1-Church. These are likely duplicates for the same event. Parishes were Rynn district and Anaduff respectively.
For Marg(aret) Cryan B 1872 ditto, I found 1 rcd in 1872, Kiltoghert RC parish.
For James Cryan B 1870 ditto, I found 1 rcd in 1870, Leitrim district.
For John Cryan B 1866 ditto, I found ditto.
For Pat(rick) Cryan B 1864 ditto, ditto.
For Bri(dget) Cryan B 1860 +/- 1 yr somewhere in Ireland, with a father forenamed John, I found 1 parish rcd for "Brigid" in Co. Roscommon, Croghan parish.
For Mary Cryan B 1858 ditto, I found 1 rcd in Co. Roscommon, Croghan parish.
For Mary Murray M 1857 (exact), Kiltoghert parish, Co. Leitrim, I found 1 rcd. A view of this marriage rcd should show the parents' names as well as other info. This data will be needed to find the pair's birth rcds.
For John Cryan M ditto, I found 0 rcds. I have found a few instances when one party to a marriage had the rcds transcribed, but not the other. This may be another. Suggest you contact the IFHF.
For Mary Murray B 1836 +/- 4 yrs, Co. Leitrim, I found 10 rcds: 1832, 1833, 1834, 1836, 3-1837, and 3-1839. Two in 1833 and 1837 were in Kiltoghert parish. One is likely for your ancestor. Father's forenames were Farrell, and Thomas.
For John Cryan B 1834 +/- 4 yrs, Co. Roscommon, I found 4 rcds: 1834, 1835, and 2-1836. None were in Croghan parish. Father's forenames were Bartholomew, John, John, and John. The mother's name should resolve this conundrum.
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.