26 x 1-1/4 (EA-1) has a bead seat diameter of 597mm. The Schwinn size also should be 597mm. Keep in mind this is not English 26 x 1 3/8 (EA-3), which is 590mm. Modern production tires should have the iso size on there, so you want the ones with 597, not the ones with 590 printed on them.
For the 590mm size there are quite a few options. Not a ton, but you'll have at least a few. For the 597mm size, it's really old stock tires or new Kendas (37-597 designation on the sidewall). You've got some strong hands if you can force a 590mm onto a 597mm rim. What kind of tire were you trying to mount? Unless it was Kenda or old stock, it was probably a 590.
A good set of Dunlop Special Lightweights in 26 x 1 1/4 will be quite expensive today. They're not easy to find. Many were well-used and not in great shape now.