Right now I'm using a cardboard box, filled with old newspapers that are stacked front to back. Even at 900 fps the 22 doesn't penetrate far, but will eventually chew through it.
I've heard that electricians putty, available at Rona or other suppliers is very good at stopping pellets. If you keep a single bullseye in one spot it will eventually load up with pellets and require replacing, but at least its silent and absorbs the pellets. No matter what you do, you want a safety back stop. I have a sheet of plywood covered with 2 layers of old carpet as my just in case, behind the target box.