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 parish, 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 Pat(rick) Meehan B 1833 +/- 1 yr in Co. Sligo with a father forenamed John, I found 1 rcd: 1833 Sligo.
For Mary Meehan B 1838 +/- 1 yr somewhere in Ireland ditto, I found 5 rcds: 1837 Armagh, 1837 Meath, 1838 Tipperary, 1839 Galway, and 1839 Westmeath.
For Ellen Meehan B 1840 +/- 1 yr ditto, I found 3 rcds: 1839 Kilkenny, & 2-1840 Tipperary.
For John Meehan B 1800 +/- 1 yr somewhere in Ireland with the father's forename unknown, I found 6 rcds with yr, cnty and father's forenames as follows: 1799 Tipperary (Laurence), 1799 Co. Dublin ("M"), 1800 Limerick (Michael), 1800 Cork (John), 1800 Dublin (John), and 1801 Meath ("Jo").
For John Meehan M 1824 +/- 4 yrs somewhere in Ireland, I found 27 rcds, with 3 in Co. Sligo. The Sligo rcds are in 1825 and 2-1928.
These dates are fairly early when rcd keeping wasn't that good. This lowers the chances that some, if any, are for your ancestors.
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.