I think for Christians, we must be careful not to depend on things of the world to do for us what we have been given the ability by God to do. And yet we must sometimes depend on others and other things to aid us in living our life to glorify Him. Even Timothy was told to "take a little wine," right? In the end, it's one of those "situation" answers, as you point out.
I am a tired mother with a very overactive 6 year old, and though I do not want to rely on drugs to calm him, I'm forced to consider it, if this is indeed a problem that might be out of his hands and ours. It is a situation which I must deal with personally, and I know that, since no one else can really know all the details of our situation, it would be hard to answer the question for us. We will continue praying and fasting to find the answer for our son, and I pray you will continue to be available to give good Bible answers to those who ask you.
Over the years, I have dealt with several "overactive" boys. Currently my next door neighbor and a member of the church where I preach has a boy whom I laughingly refer to as the Dennis the Menace poster child. He never intentionally does anything bad, but there is never a dull moment around him. His mother states that she was a hyperactive child and this is payback time. They chose to not use drugs in his case, though I'm positive she could have gotten them with no problem. But she is a nurse and realizes that the same drugs that calms a child also dulls the mind. He is turning out to be a brilliant boy, as most overactive boys are, but first everyone around will need to survive his childhood.
One of the best advice that I can give you, whether you chose medication or not, is to get your son involved in as much activity as you can. Wear him out each day. The physical activity actually causes a calming side-effect. One time the neighbor boy was over our house, as he often is, and was literally bouncing around and talking at hyperspeed. My wife asked him if he ever ran around the block. "Sure!" How many times do you think you could go? "A dozen easily." Why, she said, I find that hard to believe. I guess you'll have to prove it to me sometime. And off he went. Come round ten he was dragging, but he made it and quietly played video games with my sons for the next few hours.
At the Tae Kwon Do place that I teach, a grandmother has a hyperactive granddaughter. She got her black belt by the age of nine. She is also involved in soccer, baseball, dance, and swimming. She is a sweet thing, but it is the sports that gives her an outlet for her energy.
Second, since he is physically active, get rid of television and video games. These things engage the mind, but they don't engage the body. An overactive boy needs to be doing things. Without the distraction of a TV, he is more likely to find outlets that involve activity.
Third, uncontrolled energy is destructive, so find things he is interested in that gives him constructive outlets for his energy. If he likes tinkering get him things to build, he might have the makings of a fine carpenter, mechanic, or engineer. If he likes plants, put him in charge of a large garden. He might be mowing all the lawns in the neighborhood when he is a teen. If he likes animals, he might be watching everyone's pets while they are on vacation and walking dogs for the elderly ladies down the street.
The one most worn out is mom because the activity seems to never end, but enjoy the days while you can and watch him grow into a fine young man. "Whatever your hand finds to do, do it with your might; for there is no work or device or knowledge or wisdom in the grave where you are going" (Ecclesiastes 9:10).