Low end to mid quality nerf guns should meet your requirements for something that does not require a lot of protection and is somewhat low cost. You will even save on the cost of BBs as form darts are reusable.
If you are dead set on an cheap airsoft gun you can try the dollar stores, walmarts or Canadian tires in your local area as they shops carry low end soft air guns. Caution even though these are low quality items you should still wear proper eye protection.
"Its only a little bit on fire"