If you ever have a patron come in and say, "You know, I want one of those books where they have pictures instead of words?"
They have a word for that! They are called Rebuses and that's exactly how you can search for them in the catalog: a word or keyword search for Rebuses and Juvenile. Using picture clues to help decipher meaning is a legitimate step on the road to reading, so don't let anyone tell you these books are "cheating."
They are in a couple of places:
The Ready-to-Read series has several TV tie in books in the Easy Reader section.
Shirley Neitzel has a little niche on the Easy Picture shelves with her books. They aren't a series with a continuing character, but each has the same cumulative-tale rebus format.
There are one or two others (Smoky has another ER series) but this should get you started! Here's a list from Allen County that may help you scrape a few more titles together. If you know of any other searches or titles that will help with this question, please chime in!