Stephanie, I always thought Schwinn S7s could only be fitted with Schwinn approved 1 3/4" tires.
But, I managed to get a set of 2.125" balloon tires to fit a S7 wheelset.
Duros is what worked. They (Duro), has a large selection of colored tires.
The trick in getting the beads set into the S7 was to not fully inflate the tire while it is being mounted.
Slap the tire with a mallet or on the floor till the bead is even around the sidewal of the rim.
Then slowly inflate till it seats.
Here is my Niece's 1958 Starlet middleweight with Duto balloon tires. The tires are a tight fit within the confines of the fender, so I had to flare them a tad. Forks were wide enough.
Sent from my SM-N920V using Tapatalk