Electricians duck seal  (You need to Login or Register to view media files and links)  or artists oil based modeling clay will do the trick.  A side benefit is that the bullets won't shatter, and you can easily melt them for bullet lead.   

It takes a couple of inches of the putty or clay to slow the bullets down.  Might have to put a piece of plywood over it to hold it in place.

dave

sticking the putty on the inside I assume. Interesting idea--with a light wood or coreplast panel to hold it up against the slope. 
  I also thought of putting a couple layers of salvage coreplast behind the paper target to slow the projectiles down a bit.
Someone once told me about taking an old circuit-breaker box, gutting it and putting a new steel back-panel in and the plastering an inch or two of Duct-putty onto the back panel would make a good one to hang on the wall.   

The snail (scroll) type is not that quiet since you are still hitting metal. Rubber is far quieter and cleaner. The snail type will still produce dust from impact.

I built a snail type years ago using some well pipe my neighbor gave me. It wasn't a perfect transition in the segments, as I started with 4" in the center, and cut it in half, and welded a 6", 8", and 10" halves to get it larger. In the final step I made bevels up and down to direct the bullets into the snail trap. I made the sides removable by simply using 3/8" all thread rod to hold the two sides sandwiched to the trap. Made it simple to split and dump the lead out when needed.
I put 3/4" plywood over the opening, as a further stop, and sound reducer. About the time I needed to change the plywood, it also needed to clean the catch area. My trap was extremely quiet, and I think partially because of the thickness of the material, as it was all about 3/16"-1/4", and the plywood to help deaden the sound.
I sold it to a friend when I moved back into the city, as the laws here don't allow me to fire a gun at my home. But if I had a silencer, nobody would have known I was shooting, as the trap wasn't noisy.

If you live in a part of the country where Mac's is located they sell sound deadening material for tractor cabs. Glue it on to the back of the trap and it should absorb the bullet hitting steel noise. That combined with a silencer should make for quiet shooting if you don't live in a commie state!

We use duct seal on our indoor bullet traps for two reasons. Noise and lead dust elimination. We build a frame that we attach a simple disposable cardboard backer to. We try to find "waxed" cardboard but if not a sheet of wax paper works. Lightly staple the backer to the frame. Then fill the frame with putty. 
This frame sits in front of a standard bullet trap that catches anything that makes it through. 1" will just stop a sub 22RF. We make our frames from 2x2 and that gives a full 1 1/2" of putty when filled. 
In use just position the target a few inches from the last course of fire. 
At the end of your shoot peel the backing off the frame with putty attached And then peel the backing off the putty
Clean the putty by bending it backwards and all the intact bullets will be exposed to pluck out. Your cleaned putty is ready to go again. Expect about a 5% loss in putty during a good shooting session, but at $1.68 per pd package it's not a great expense

I should not admit this but, I was shooting subsonic 22's at (3) layers of high density ply from my dining room table to the living room(almost 50ft). First shot.... loud crack at contact and base of .22 showing flush with 1st layer of ply. The next 6 shots got successively quieter at contact. I was thrilled at the one hole group until I started checking the ply. Shots 3-6 went thru the ply, the drywall, the insulation, the sheathing and then the vinyl siding to escape and embed in a 4ft oak outside the house. Lesson learned.