Saddle ring

A saddle ring is a metal ring attached to the receiver of a rifle or carbine allowing it to be tied to a saddle or used with a special sling. Saddle rings could be attached directly to the firearm, or in some cases to a saddle ring bar, which allowed the saddle ring to slide along the action, such as on the British Enfield P1856, a short cavalry version of the Pattern 1853 Enfield used in the American Civil War. Virtually every carbine-sized weapon used in the Civil War was equipped with a saddle ring and/or saddle ring/bar. Saddle rings are most commonly found on lever action rifles and other firearms of the late 19th and early 20th centuries that were suitable for use on horseback. The muzzle of the rifle was placed in a carbine socket or boot. The idea behind using the saddle ring, and its carbine sling, is to allow the mounted soldier to never be separated from his weapon.

Modern Makers of Carbine Slings
Junior's Carbine Sling:

http://www.castbullet.com/srsling.htm