Schwinn tires for that bike would be 26 1 3/8-1 1/4. If that's what you have, it's an odd size and best I can tell the only tire available is a Kenda. The ISO diameter of those rims is 597mm and they are either S-5 or S-6 -- I think S-6. If that's what it has, they will be steel and somewhere on them they will say Schwinn and probably S-6. My wife has an old Schwinn Breeze and I found those markings on the rim when I trued the wheels. But, I agree with rhenning that the bike probably does not have the Schwinn rims -- probably has what is called EA3, or 650a, which is a rim with a 590 mm iso diameter. Tires for that rim are, best I can determine, all 26 1 3/8 (no other widths seem available) and are readily available from many manufacturers including Kenda, Panaracer, Michelin, and Schwalbe. You can find Kenda tires in that size for $10 with free shipping on Amazon but someone says that they are actually mislabeled 27" tires and won't work. Harris cyclery has a good rundown n these tire issues.

Looking at the pictures, I can't tell if those are the old Schwinn rims or not. They don't appear to be quite the right shape for a Schwinn rim, but they do seem to have the "knurled" embelishment along the middle of the rim. Probably going to have to measure if you can't find some markings on the tire, rim, or tube.