I made my own leather boot for the stock of my CVA Mountain Stalker and then padded inside the boot so the recoil was not so brutal when shooting stiff loads. I could have just as easy left one end longer and had a sling attached there, but I didn't. Instead I cover the leather boot with a black wool sock. When the sock is dirty, I wash it. It covers and holds the boot in place, and also matches the composte stock of the rifle while taking the recoil out of the stiff loads.
Go ahead and make the boot. If your not happy with it, then don't show it off...

Actually the traditional way to carry the rifle was in a wool gun sock (full length). This was done to protect the rifle and the charge in the rifle. Some of those gun socks did have carry slings. Sure would slow a fellow down if he needed his rifle in a hurry.