Years ago me and a friend used a large piece of carpet draped over an old swing set. The bow I was shooting at the time was around 80lb draw and would blow through it from anything less than 40yards but everyone else I shot with had no problems.
Cheap and easy backstop. Trailers that are sold by Lowe's are shipped without tires, so the hubs sit on styrofoam blocks. My local lowes puts these blocks inside of one of their cargo trailers on display. I asked the manager and he gave me some for free. I simply took six of these blocks, taped them together with duct tape and you have a 3 x 2 backstop that is about 10" thick.