I have been using 3-4 inch thick cardboard boxes filled with old once-folded newspapers stacked on each other until the box is completely full and taped shut with shipping tape. Both the boxes and newspapers are free since you are going to put them in the recycler anyway. Have one that has over 500 shots fired into it and it just keeps going and going. If the entry hole gets too chewed up, just patch it with shipping tape and keep at it. This is minimized by just moving the targets around to different positions on the box.Have used this with a Ruger Air Magnum in .177 and a RWS350 in .22 and a pellet has yet to get to the back of the box.
Mark, I use an 8"x10" (4" deep I think) steel electrical junction box from Home Depot which I have filled with electrician's putty, aka: duct seal. I also get the duct seal at Home Depot which comes in 1lb bricks. I tape standard 8.5"x11" letter size target papers on it that I print from web sites on my home printer. This trap is completely silent and I have put well over 1,000 pellets through it. Maybe 2,000. It's a little heavy and getting heavier as I put more lead into it, but not bad. If the pellets ever start going through the duct seal, the heavy steal construction of the junction box will stop them with no problem. I made this silent trap almost 3yrs ago, and have not had to replace the duct seal yet. It is two (2) 1lb bricks deep. There is about 15-16lbs total duct seal in it. It will trap pellets from Magnum Springers, Maurader, etc. up to 30-35fpe with ease. For the 3 65-90fpe Condors I use a 7.5"x7.5" ball (now square, hehe) of duct seal. I don't hardly target shoot indoors with the Condors, but shoot them regularly through the Chrony.Duct seal is not a very inexpensive option, but well worth the $ IMO. Duct seal has served me very well over the years and it's completely silent. It amazes me how many shots it can handle over and over in the same spot from my 350 .22, and still has not penetrated all the way through anywhere as far as I can tell. If it did, the heavy-duty metal junction box would stop the pellet but it hasn't happened yet.
Newpaper or any paper will not be as silent, and therefore not as backyard friendly, as electrician's putty. This is a central issue for many of us.