First, airsoft has no real accuracy- smoothbore, as are almost all BB guns. Pellet guns, OTOH, are eerily accurate. They DO make pellet traps that are intended to catch those, and they can be used indoors.
http://images.search.yahoo.com/search/images?_adv_prop=image&fr=slv8-hpd10&va=airgun+pellet+traps
There are also cartridges made for indoor target use- no powder, plastic bullet, reusable. Cardboard box with crumpled newspaper for bullet trap.
http://www.speer-bullets.com/products/components/plastic_training_bullets.aspx
There are also lasers that can be used for practice. Or build your own....
http://www.instructables.com/id/Laser-Shooting-Range-laser-guntarget/
Back in the early dawn of time, the military used a Holifield Dotter Cartridge for training- firing pin made a small rod pop out of muzzle, and make a dot on a paper target a couple of inches from the muzzle. Make your own, using a pencil with masking tape rolled around it to to make a loose fit for the barrel. Sounds simple, but may be harder to get those dots to converge than you think.