I think the sizing you mentioned may not be what you are looking for. my kids are currently riding the 24" MTB style bikes. the size under the full adult MTB size. I just got them used cheap cuz I knew it would only be for a few quick years. turns out they are going on their 3rd season with them. last year I got them these tires for less rolling resistance. I crank them up to their MAX pressure:
Maxxis Holy Roller BMX Bike Tire
http://www.biketiresdirect.com/pmbh2...24_tire/pp.htm