Hello Bill,
Your revolver is a Remington Rider Double Action Pocket Model made from 1860 to 1873 in 31-caliber percussion and post 1873 in 32-caliber metallic cartridge. According to Flayderman’s guide to Antique American Firearms approximately 2000 total of both types were made, however in the Guns of Remington the number stated is 8000. In either case it would make yours a fairly early one. They were made with both a blue finish and later ones were nickel plated. Yours was probably blue since it is an early one. As far as I know there are no production records available to determine the manufacturing date. With the small number manufactured I would say your chances of finding an original cylinder pin are slim to none. You might try some of the parts dealers listed on the RSA home page under Service/Parts.
Hope this helps,
Bill