Use two or three large nested cardboard boxes (often free at "big box stores"), and line the inside back with another 8 or more corrugated cardboard sheets. Even my low-powered BB rifle can send a round that penetrates 4 or 5 layers from 33 ft. The pellets from the pumpers can easily exceed that, but not many make it past 6 sheets with my guns at their chosen power levels. You could hang a mat or scrap carpet in back of the cardboard box, which should suffice for any pellets that make it past 10 sheets. Because after a lot of shots, there will be large holes that align across the sheets, replace holey sheets frequently.
All that cardboard also dampens the impact sound. The expulsion/shot noise is a different worry.