The RI Cemetery Database has Betsey's year of birth as c1785. She was age 67 in the 1850 Federal Census, which would suggest a birth year of c1783. The date of death in the cemetery data is 28 March 1866; the NASDAR Report of General Records, 1959, p. 57, Bible record of the family of John & Mary (Arnold) Stafford, has Betsey's date of death as 10 March 1866.
The book "Descendants of Roger Williams, Book I," the Waterman and Winsor Lines, p. 71, also gives the parentage of Betsey Stafford. It says she was born 1785, and married Alphonso Armington and/or Charles B. Remington.
In the 1860 Federal Census, Betsey Remington is age 76, living in Cranston, RI, with her son Benjamin W. Remington and his family.