Personally I think the trick is to deaden from inside using rubber mulch....but its all about what works for the individual......I put mine on its back and stuffed it with mulch ...then taped a piece of corrugated plastic across the front to hold the mulch in...I tape my targets to it.....last a pretty good while...when it gets perforated I tape a fresh piece over existing piece...good luck
I just recently did this with my trap. I just used stuff I had lying around: silicone caulk and rigid foam insulation. Works incredibly well in my 15ft basement range. I swear I would hear more from the report of the guns than I do the impact. Another great advantage to the materials I used is that it really didn't add any significant weight to the trap.