Are you sure that it's 24 and not 27. I ask because adult varsitys had 27" wheels, but there might have also have been a 24" version.

The 27 x 1-1/4 tires are standard and any 27" tire will fit, but on 26" and 24" Schwinn used a proprietary size, ant those tires are hard to find today, and there's no latitude for an alternative. You may refer to this size chart Sheldon Brown compile a few years ago for more info.

Note, if there's any confusion, see if you can find a ISO size marking on the tire which is formatted as 123-45, or an S-5 molded into the tire. These are very specific and tell you exactly what you need.