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 Charles Colville Horrocks I found an M rcd in 1869, Co. Armagh.
For Helen Alice Miller, I found ditto.
A view of the detailed M rcds SHOULD show their parents' names and other info.
For Helen Miller B 1846 +/- 4 yr somewhere in Ireland with a father forenamed William, I found 0 rcds. Magistrates and other civil functionaries were often assigned to Ireland from England, or were local Protestants. Hence, her origins may have been English. England was performing censuses and had civil B/M/D registration slightly before her birth date. Suggest you search these rcds.
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.