Mouthpiece caps are pretty cheap. The equivalent sax mouthpiece cap that would fit would be from a bass sax but it's not likely that any of those would be laying around.

Any local music store should have one for vary little. They might even give them away for free. An alternative is... uh... I don't know any alternatives.

Why are you doing this anyway? I think that if it's a school instruemnt it's their responsibility to ensure that it is complete & working before it is given to you to play.

I would suggest if they're going to buy a mouthpiece cap, ask them to get a new ligature as well - mine came together, and the difference to the sound can be incredible!