Shirley,
This is most interesting! The John Doyne/Doying I mentioned before was a grandson of Francis Doyne/Doyen whose father was also a Francis. There are many descendants with the name of Francis. The above John's mother was a Mary, he had a sister, Mary, but his birth is found: Extractions of Vital Records of Vermont, Book M. 1, page 223. Rygate. (FHC Film # 027534). Name spelled DOYNE and DOYEN. Birth 8 Dec 1807 in Ryegate, Vermont. I just looked at the 1850 census for your John Doing, Nancy and son Francis, and see that it gives his birth as New York. So the places and dates don't really match.

I do have another John Doying who was born abt 1813 in Canada, but the birth of his second child Sarah Jane Doying (both children were daughters) is recorded as follows: Birth and bapt. - La Societe de Genealogy des Cantons de l'est Inc. Anglican Church, Sherbrooke [Quebec], says: daughter of John (deceased) and Allis Potter, Kingsey QC". So he is out because he had died previous to your John on the tax rolls and census.

Perhaps we are just grasping at straws, but I have often wondered if the "Doing" names I find are related. Following hunches sometimes results in a good outcome. If nothing else, we might elimanate the possibility of a relationship between the families.

Good luck!
Barbara