I was looking for some old time radio stories, but I'm not really sure they're out there for young ages. The closest really good radio show that I found was a 1950 Lux Theatre recording of Wizard of Oz and another Miracle on 34th. Anyway, if you can find some good stories or your child is old enough, there might be some nuggets that are great to go with the actual book.
you can also try
http://www.kiddierecords.com/ but I haven't spent too much time listening to the various records; some may be better than others.... but at least it's free!