Stephen is in the 1850 census at Tiverton living with his family. In the 1860 census he is age 14, and living at Little Compton with Benjamin Pearce the elder and his wife.
In the 1870 census, Stephen is age 22, a farm laborer, living at Tiverton with the Gideon Durfee family, next door to Amanezer & Olive Durfee.
The Roll of Militia in Tiverton, located at the town hall, lists Stephen Remington for the years 1871, 1872, 1873, and 1874. Also listed for 1872 is Henry H. Remington, who is probably Henry Hale, a distant cousin.
There is a marriage record for him at Newport -- NeM 1-131; I haven't checked it yet.
He is very likely the Stephen Remington aged 67 living at Fall River in 1910, with a wife named Elizabeth aged 60 and an adult daughter Minerva, aged 38. Living with them is brother-in-law Albion Grinnell, 51. By 1920 Elizabeth is widowed. I believe she is Elizabeth Grinnell, so I have entered her family information as such, with the assumption that she belongs as the wife of this Stephen Remington.