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 Peter O'Malley M 1861 +/- 4 yrs somewhere in Co. Mayo with the father's forename unknown, I found 2 M rcds: 1861 and 2-1865. There aren't many Peter O'Malleys in Co. Mayo. One of these MAY be for your ancestor. The 1865 dates seem to fit your timeline. It was best to immigrate early in the marriage B4 there were many children. A view of the M rcds SHOULD show which, if any, had a bride named Honor(a).
Suggest you search U.S. censuses for relevant decades to see if Mary Ellen had siblings - if she wasn't the eldest child, this could alter your timeline.
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.