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.
There are also cartridges made for indoor target use- no powder, plastic bullet, reusable. Cardboard box with crumpled newspaper for bullet trap.
There are also lasers that can be used for practice. Or build your own....
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.