In the 1850 Federal Census, Stephen Remington and his wife Sarah are age 50; son Orville is 9, and daughter Mary is 5. They are living in Ward 4, Providence, RI. In the 1870 Federal Census, Stephen W. Remington is age 71, and Sarah R. is 70. They are living in Ward 7, Providence, RI. Their son Orville, age 29, is with them. Thus, Stephen's date of death in the RI Death Index can't be correct (8 May 1863). Therefore, I am changing it to 1873.
He is probably the Stephen W. Remington who is in the Providence City Directory of 1836/7 as a cooper.