Hoyt Ruckus JR or Diamond Atomic - both super adjustable in length and draw weight - both under $200. (Make sure you have someone who knows what they are doing set it up correctly for you - should be no extra charge for this from where you buy it)
DO NOT buy one of the $69 plastic bubble package chinese bows with plastic riser and limbs, cord for a string and very little if any adjustablility. I get so many disappointed kids in the shop who's parents try to save $$ and get them one at a box store and can't get them to work right, bring it to me and find out they bought junk that won't work right. Bow shoots like #^@%! and they end up in a dusty closet and the parents think "my kid just doesn't like archery." Fact is if they get a good bow the kid will love it and use it a lot more.