What is a sensible dosage of melatonin to give to a 6 year old boy with problems falling asleep?

None: Melatonin should not be used for sleep onset issues for a six year old. I would address other issues like sleep hygeine, activities leading up to bedtime and limit setting...

Why?: Try to pin point why your child has trouble falling asleep. Does he take naps in the afternoon? Maybe limit them. As a rule, limit vigorous physical activity several hours prior to sleep. Also let the brain "wind down" by turning electronics off and dimming lights 45 min prior to bedtime. Do not eat prior to bed.