Welcome to Ireland Reaching Out!
The Croagh RC records start in August 1836 https://registers.nli.ie/parishes/0880 I searched on the subscription site Roots Ireland and did not find a baptismal record for Michael so likely he was born and baptized prior to 1836. I did find a likely baptismal record in 1839 in Croagh for Agnes Christy. Did Michael have any younger siblings?
Name:Agnes ChristyDate of Birth:
Date of Baptism:04-Mar-1839Address:?Parish/District:CROAGHGender:UnknownCountyCo. Limerick
Father:William ChristyMother:Ellen O'BrienOccupation:
Sponsor 1 /
Informant 1:Tom Walsh Sponsor 2 /
Informant 2:Ca Walsh