507 rims on a narrow frame
The bigger problem here isn't the width of the rim, it's the sizes of tires made in that ISO.  As mentioned in the comments, frame width is another restricting factor.  Junior Cruisers are made for junior riders.  If he's outgrowing it, it may be time to switch up to standard Cruiser or Pro 20" class.  To answer your question, 507 ISO rims are usually between 19 and 24mm wide.  They will run tires from 24x1.25 up to 2.25 and a little bigger for the larger side of the range.  One other consideration is brake position.  Make sure you can get brakes that will reach the(farther) rim position.