Looking around it appears that the scientific basis for this is in the caffeine, but herbal remedy type people are reporting that decaffeinated green works as well. They also talk about adding chamomile and/or other herbs as well; of course they claim great results.
Some of these might be worth looking into, however I would personally think it extremely irresponsible to try them on a child based solely on personal recommendations from anonymous people on the internet, or homeopath type people with no medical training - check with a doctor before doing anything, find out what the herbs are, what they do, how they work, and if there's any kind of side effects or interactions.
Tea (real tea, Camellia sinensis) on it's own, however, is probably
a good thing to give anyway, particularly if your doctor is already aware of it.
As far as the caffeine, remember that L-Theanine can counteract the negative aspects of tea. You might actually try some of the green oolongs that are thick and sweet. That thick, sweet, veggie-protein taste that makes the tea viscous and gives it a meaty texture that makes you want to chew is the L-Theanine, which is an amino acid. This is not only good for you, but it will relax you enough that it should prevent the caffeine from keeping you awake. I bet he'd also like the flavor better, too
I've drank large amounts of this before bed without being kept awake, but then it should probably be kept in mind that my caffeine tolerance is most likely much higher than a child's or someone that isn't accustomed to taking in much/any caffeine. It's worth a try, anyway, as it's not going to be much different from green tea in any significant way.