Carpet would work great for an indoor target. If left outside, it would be full of mold in a matter of weeks.
I stopped at Sears last week to pick up my Dad's new mower, and noticed a few large plastic bales sitting outside. Apparently, they sell the bales for upwards of $300 each to recycling companies. I asked if I could have one of the bales since they were just sitting outside, and the associate said to come back after close and take what I want. I'll need to round up a few guys and go grab one next time they are out there.