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 Mat(hew) Murphy B 1841 +/- 4 yrs, Co. Armagh, with the father's forename unknown, I found 2 rcds: 1838 Tynan parish and 1840 Lower Killeavy. Father's forenames were Michael, and John respectively.
For Hugh Murphy B 1892 +/- 1 yr, Co. Armagh with a father forenamed Mat(hew), I found 1 rcd in 1892, Lower Killeavy parish. This is likely your ancestor - no guarantee. A view of the detailed rcd SHOULD reveal the known parent's names.
For Daughter 1 Murphy B 1874 ditto, I found 3 rcds: Bridget 1874 (Kilfree & Killaraght parish), Mary 1874 (ditto), and Mary 1875 (ditto).
For Daughter 2 Murphy B 1879 ditto, I found 5 rcds: Bridget 1878 (Kilfree & Killaraght), Bridget 1879 (Killoran), Joan 1879 (Kilfree & Killaraght), Bridget 1880 (Kilfree & Killaraght), and Cat(herine) 1880 (Killoran).
You will need exact (DOB), parent(s) name(s), and/or placename(s) to pick which, if any, of the daughter rcds are the correct ones. Since you KNOW the mother's forename, this should be sufficient. Views of the detailed rcds usually reveals the parent's names.
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.