Hi and welcome to RootsChat

I cannot see a birth for Mary unfortunately. With her birth being before the start of statutory registration, at best you may find an entry in the Old Parish Registers for her birth and/or christening. Can't see one though

Mother Susan may have simply not registered her birth or arranged for a christening (only about a third of BMD events were registered pre 1855). Lots of other reasons too why you may not be finding her entry.
Did Susan show as unmarried in 1851? Mary Tait and a William Thomson, aged 4, are showing as boarders with Susan in 1851. Was William a brother to Mary?
Possible separate entries for Mary and Susan in 1861:
Mary Tait, 21, domestic servant b. Girvan at the Balig Farm House in Ballantrae.
Susan McClellan, servant, b. Girvan at Jellestone, Coylton.
Monica