My kids bowl in leagues and when I was looking for shoes for them I had a really hard time finding reasonably priced children's shoes. Our pro shop didn't carry any and the man working there said he wouldn't even buy his own child them because they're so expensive and children grow so fast that you don't get your money's worth from them.
I ended up getting DS's from ebay and DD got hers as hand-me-downs from her coach's daughter.
A little OT, but if you're children enjoy bowling you should consider a league. My two oldest have been doing it for about 5 years now and they also choose to bowl in tournaments (you don't have to in order to be in the league) and have a little bit of scholarship money put away from their winnings. They have a blast, it's good exercise and fairly inexpensive compared to other sports, we pay $32 a month at our bowling alley. Skill level also isn't an issue, they have coaches and "handicap" scores.