This is the record from James N. Arnold's VRs: REMINGTON John, July 29, 1754. It is out of date order among the children. I have not seen the original at Cranston, but maybe it is 1774, which would be the correct order.
BSR's ancestry chart has the incorrect birth date for this John, with no marriage noted. He says that John was at Argyle, NY, in 1790 and at Litchfield, NY, in 1800. That may be correct. The 1790 census shows a John and a Stephen Remington at Argyle.
I don't remember my source for this marriage to Mary Green -- probably the DAR Patriot Index (needs more research). However, the death date of 1840 may be incorrect for this John Remington, since the other one (b. 1756, s/o Thomas & Abigail of Warwick) died in 1840. Someone may have confused the two John Remingtons, both born in RI around the same year.