I accidentaly found this glitch while bored one day. To make Fry invisible (might work on other characters but not sure-haven't checked yet) turn on the invincibility cheat then use a suicide booth. The game will mess up, the booth will make you invisible.
Note: Unfortunately the only way to fix this glitch is to turn off the invincibility cheat and either re-use the suicide booth or fall of a huge cliff to kill yourself. It can also become a bit confusing and annoying after a while.