Let's talk Kevlar or Dyneema!

I think a soft urethane rubber (with a shore hardness of 30) would do ok for reducing the impact noise or vibration but you would still want something strong behind it (like hardened steel) to stop the pellet getting through. 

Urethane rubber is fairly cheap. It comes as a two-part liquid and it will easily stick to a sheet of steel or anything else you pour it over. 

If the layer is thick enough, it might even catch the pellets. 
 
"T3PRanch"If you recalled I inadvertently proved that 1/2 Ton Truck Radials are not the least bit impervious to .25 Marauder fired JSB Heavy puncture at 25 yards. Shhh! My wife has almost forgotten that incident. Might want to use better rubber than that. lol

Thurmond
Rubber won't stop the pellet penetrating but it will reduce the noise if a layer of soft rubber is used over something that will. It would stop the loud vibration noise you get with an impact on steel.