No sign of a mother's name of any of the certs for your Mary ?
If you have parents names you can sometimes get the search started by locating younger siblings (i.e. born after 1864) in civil records.
You didn't mention a denomination for your Callaghan/Callahan family but if they were RC and Mary was baptised in for Castlebar then the name of the parish to check is Aglish.
Callahan is a reasonably common surname so there are a number of potential matches showing up on the index on Co. Mayo parish records on
RootsIreland (pay-website). None seem to be in exactly 1853 or 1856 (both mentioned above?) , but you have to allow a few years either way when searching, as dates of birth, ages etc given on later records are not always accurate.
One of the baptisms showing up on the index is a Mary Callahan in 1851, in Aglish, father's name seems to be matching on John - so might worth following up to see if mother's name, siblings etc agree with the clues you have from your US research.
There is a closer match by father's firstname and the 2nd date you mentioned, with a baptism of a Mary Callahan in 1858, but not in Aglish/Castlebar aprish.
An RC baptism from that timeframe would usually include full names of the father and mother, name of the child, date of baptism plus the names of two godparents. Sometimes a place of residence - possibly the name of a townland, or in this case might just have 'Castlebar'
(Note the RootsIreland website may not have all available records for the county, and the index is sometimes incorrectly showing Gallagher as a possible variation)
Moderator Note : moved post to Co. Mayo as that where Castlebar is located.