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I think the wife of Terence Cormack was a Mary Noone. See record below from Kiltane RC parish. Records for that parish start in 1860 https://registers.nli.ie/parishes/0741 Roots Ireland has a record for a John in 1862, a Mary in 1863 who likely died young and the second Mary below. The other children must have been baptized prior to August 1860.
Name:Mary CormackDate of Birth:
Date of Baptism:10-Dec-1865Address:GortbrackParish/District:KILTANEGender:FemaleCountyMAYO
Father:Terence CormackMother:Mary NooneOccupation:
Sponsor 1 /
Informant 1:Andrew Healy Sponsor 2 /
Informant 2:Mary Cormack
Patrick Coyle and Bridget Gallagher were married in 1874. Here is the civil marriage record which also shows the names of the fathers of the bride and groom.
This may be a son of Patrick and Bridget.
Name:Anthony CoyleDate of Birth:13-Oct-1883
Date of Baptism:14-Oct-1883Address:GortmeillaParish/District:KILCOMMIN ERRISGender:MaleCountyMAYO
Father:Pat CoyleMother:Brid GallagherOccupation:
Sponsor 1 /
Informant 1:Anthony Coyle Sponsor 2 /
Informant 2:Mary Gallagher
By the way, if yoyu did not know, www.irishgenealogy.ie is a free site which has civil birth records from 1864-1916, marriages from 1870-1940 and deaths from around 1880-1965.
Let me know whatb additional questions you have.