Looks like a standard padded sling. The butt stock cover looks to be cut to allow the sling stud to stick through.
Here is what you would need.
Stock Guard
http://www.beartooth-products.com/shop/vmchk/stockguards-rifle.html
Sling
http://www.beartooth-products.com/shop/premium-slings-rifle.html
Swivels scroll down the set for Ruger Carbines.
http://www.grovtec.com/products_rifles.php
You will need to drill the stock to install the rear swivel stud. The front installs on the barrel band with no modification. Should not be too hard to drill a 96/44 as the stock is flat not rounded.
If you don't want to drill still get the set and only install the swivel stud on the barrel band and then get this.
http://www.outdoorconnection.com/products.cfm?page=details&cat=Sling&sub_cat=Padded%20Total%20Shotgun%20Sling&name=The%20Padded%20Total%20Shotgun%20Sling
This sling attaches at the front swivel but wraps around the butt stock with velcro. I use them on my shotguns they work great. You would not need the magazine cap if you contact them they might be willing to sell just a sling.