How cheap? Fiberglass is probably the best performing simple material with no extra design required, and is moderate in price. Not really cheap, though. You'd want something between 3-6 lb.pcf stuff. Buy more and treat your first reflection points, too.
Cardboard egg crates are reputed to work well but is unsubstantiated by measurements - see this thread:
http://www.audiocircle.com/circles/i...?topic=31134.0
Russell Dawkins is a pretty experienced recording engineer, and I take his comments seriously. This may not work well with your door situation, though.
Foam is something of a fire hazard, and measurably only performs well at frequencies above 500hz or so. It's a viable alternative, but fiberglass is much better performing in the bass region.
If you can afford it, though, and that door is never used, a foot of fiberglass should do wonders. You just need a way to make sure you don't ever beat that fiberglass with a stick because it's really irritating. Your local warehouse store might have rolls of fiberglass, stacking 5 or 6 of them up to the ceiling might also be a quick and dirty way to solve the problem. You might not even have to take off the plastic wrappers, high frequencies should bounce off of it, keeping yours in and theirs out, and bass will be absorbed. If you do deal with rigid fiberglass, you need to wrap it in something like burlap and make sure no one beats it with a stick. Don't touch it with your bare skin, either. Quite irritating.