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 Dan(iel) Harte B ???? somewhere in Ireland with the father's forename unknown, I found 1 rcd in 1836. The parish was Sligo RC. The father's forename was Pat(rick). A view of the detailed B rcd SHOULD reveal the mother's name.
For Pat(rick) Harte B 1830, Sligo parish, Co. Sligo with the father forenamed Pat(rick), I found 2 rcds: 1831 and 1833.
For Eugene Harte B 1845 ditto, I found 1 rcd in 1841.
For Eliza Harte B 1843 ditto, I found 0 rcds in either Sligo parish, or in the other Sligo parishes.
For Marg(aret) Harte B 1836 ditto, I found 1 rcd in 1840.
For the surname Harte, there are 1,635 B rcds compared to 12,762 Harte rcds in all Ireland in the database.
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.