I noticed a John and Martha "Beton" on the LDS site familysearch.org, with children of the same names you mention. I didn't see any birth or marriage locations or info on Mary's parents, but John has a birth year of 1722, and his daughter Mary has birth date listed as Aug 24, 1748.

I know I have Beeton research that goes back to Connecticut -- I will check to see if anything turns up.
-Carol Beeton