I had an old Irving Kaye barbox a couple of years ago and made a couple of efforts to quiet the ball return in mine. The whole ball return system was very thin aluminum sheet metal channels, that dropped the balls down onto a thin piece of particle board. It was loud as hell and drove my wife nuts whenever I wanted to shoot a few racks. Gluing cloth in the aluminum return channels didn't do much, since the slope of the channels wasn't very steep and when the glue loosened up, balls would get stuck... Only way to get them out was to remove the slate.... Waste of time.. Oddly enough, I ended up using a rubber based roofing material to quiet mine down. Worked awesome. I re-routed the path of the ball return as well. Since it was a barbox, designed for a 2 3/8 cueball, it would take 10 minutes for each ball to come down into the rack area.
What you want to keep in mind is vibration is what causes noise. Knowing this, you don't necessarily have to put something on the ball path of the return to quiet it down, you can put something on the outside of these aluminum channels to dampen the vibration and quiet the return down. The same principles apply to sound deadening your car, particularly for stereo enhancement.. One thing to be mindful of: make sure you don't cover the cut-outs in the return for chalk to drop down through. Those holes in the return channels are there for a reason. This roofing material is just one option.. You can use any number of materials. High density foam or rubber materials will work well, but there are other things that will work as well. You just have to be creative.. Look at the leather inserts that are being sold for the Delta 13 racks. They do a fine job of dampening the racket that those racks make.
Best of luck to you.