Tunstall married, about 1750, Elizabeth, daughter of John Dodsworth of Thornton Watlass, Yorkshire, by his wife Henrietta, daughter of John Hutton of Marske, and sister of Matthew Hutton, successively archbishop of York and Canterbury. His widow moved to Hadleigh in Suffolk, and died there on 5 December 1772, in her forty-ninth year.
Elizabeth
Henrietta