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. Co. Donegal and Derry were just 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 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 Bridget Heaney B 1876 (exact), Co. Derry, with a father forenamed William, I found 1 rcd in Dungiven RD.
For Marg(aret) Heaney B 1874 ditto, I found 1 rcd in Dungiven RD.
For Pat Heaney B 1871 ditto, 1 rcd Dungiven RD.
For John Heaney B 1869 ditto, ditto.
For Ann(ie) Heaney B 1866 ditto, ditto.
For William Heaney M 1864 +/- 2 yrs, Co. Derry, I found 1 rcd, 1865, Glendermott PR parish. I couldn't find a matching M rcd for a Nancy Murphy. They may have married elsewhere, the bride's name may be wrong, or the rcds have been lost to time.
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.
Hope this info adds a bit to your knowledge of your family history.