Thanks for the replies.
Apparently it is a children's bike, which kind of bites, but at least my wife is fairly short, so maybe it won't be an issue. The rim definitely says 24 x 1 1/4. I'll have to check back about the S-# to see if it's stamped on there. I'll also try to get a picture up on here this weekend. As far as cleaning up the tires to see the size, that won't be possible. They are extremely worn down and dry rotted to the point of any and all writing being illegible or non-existent. Anyways, I appreciate the help and will try to get pics up as soon as I can.