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I checked on Roots Ireland for a baptismal record for Mary from 1837-1857 but got no record. I did a similar search for William but did not find a record. You did not mention the religious denomination but if they were C of I from Galway city, you may want to contact the local church. http://ireland.anglican.org/information/dioceses/parish/14160 Available RC records are on Roots and I was unable to locate a reocrd.