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The Kilfree RC baptismal records start in May 1873. I located a transcription of Catherine's record on the subscription site Roots Ireland. See below. You will not find a baptismal record for Mary only the civil birth record. Ninth record on the page https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1872/03243/2188345.pdf
I think your assumptions about the names are logical but we won't know for sure.
This may be the marriage record for Mary Carberry See second record. marriage was in Boyle. The father was shown as John which matches but can't sure https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1912/09908/5600547.pdf
Name:Catherina CarberyDate of Birth:
Date of Baptism:05-Jun-1874Address:
Parish/District:KILFREE & KILLARAGHTGender:FemaleCountyCo. Sligo
Sponsor 1 /
Informant 1:John CarberySponsor 2 /
Informant 2:Bridget Carbery