A gravestone in Strathaven Cemetery bears the following inscription :
1771 THIS IS THE BURIAL PLES OF ROBERT JOHN MATHOU AND JAMES CRAGS ALL BELONGING TO AVENDALE PAROCHAS ALSO WILLIAM CRAIG IN BANKEND
(The OPR records for Avondale show an entry for "Mathou son to William Craig in Bankend April 47th 1755")
This last named William Craig could possibly be Alexander's father.
Assuming the usual naming convention, Alexander's mother would be named Margaret.
Alexander and Elizabeth were married in Avondale on the 13th of December 1783. (Transcribed from OPR Ref. 621/2, FR361)
Elizabeth Craig is mentioned in the OPR entry as being "in the parish of Loudoun"; that is, from Ayrshire.