I'll quote SirMike.
It is best to use bead seat diameter in talking about U.S. lightweight tires before the 1960s.
The early Schwinn rims have a bead seat diameter of 599 mm and take tires known as "26 x 1.375". That size is an archaic U.S. lightweight bicycle tire size that has not been made in decades. They are hard to find and usually hard as stone when you do find them.
However, there's a good chance you can use the new production Schwinn S5/S6 pattern tires. Kenda makes them. These have a bead seat diameter of 597 mm (26 x 1 3/8 Schwinn size, not English). That 2 mm difference usually is not enough to throw off the fit, unless they rims have high sidewalls. I'd try the modern Schwinn S5/S6 (597mm) tires on it.
If the rims have high sidewalls, you need the old-type 599mm tires, but the Superior rims, at least all the ones I have seen, have normal sidewalls.
The Superior rims are relatively valuable. The wheels set as a whole might be valuable as well, depending on the hubs and spokes. Schwinn had some premium hub options (especially the high flange stuff or duraluminum shell stuff) and some really good quality, double-butted spokes. What does the wheel set look like?