I have posted some regarding this issue in the past. My children were certified (junior certs) when they were 12 years old. However, I limited their number of dives and their depth. I only allowed one dive trip per year and their depth to 40 ft. Why?
It is well known that Nitrogen can be absorbed into the bones. Kids have softer bones then adults, so it is very likely that more nitrogen would be absorbed into their bones. Bones are not completely formed until you are in your early twenties. So, it is obvious to me that lots of diving and deep diving when you are young can damage your bones (my opinion only, there could be some studues out there, I don't know). In any case although I love to dive and my kids love to dive, I did not want them being the guinae pigs for research on how much damage nitrogen does to growing bones.
I also believe that kids younger than about 12 should not be on SCUBA. Let them learn how to snorkle or really free dive until they are old enough to pay attention in SCUBA class and understand the repercussions of DCS. Even then, you, as the parent, need to determine if the individual child is really mature enough to be a safe diver. If I was an instructor, I would be extremely careful about certifying children to dive.