What foods would help increase growth hormone levels in children so they'll grow taler?

Growth hormone. There are no dietary stimulants for growth hormone production. Optimal nutrition will allow a child to reach his/her genetically determined stature. Adding extra growth hormone will not increase that stature, but only accelerate the rate of attaining that stature.
Growth hormone. Whatever shaquille oneill eats! seriously -- we don't know of anything specifically. Good nutrition overall and adequate sleep (8-10hrs/night) during active growth years is the best advice.