I've typically in the past kept the throwable zipped into a Murray's tramp bag hooked to the tramp in front of the back beam. A quick zip and the throwable is out. The thing is whether you have a line ready to deploy to retrieve anybody hanging on the throwable.
Assuming everybody is wearing vests, there are a couple of options/thoughts.
One is that having a West Marine throw bag in an easy to grab place is a good thing. Practical Sailor rated these very well, you basically hold the line and throw the bag. Comes in 50' and 70' models. Velcro strap that to the boom or in some other easy to grab (and remember) location. I think having a velcro closed tramp pocket added for just that would be a good idea.
The other is that even though people may be wearing a vest, the design of the vest and the size of the person may mean that the extra flotation from a throwable might be a helpful thing, especially in waves. I'm guessing your boy's vest floats him pretty well, but something to consider.
Another is think about and plan for such situations when you're not on the water and think about how you would handle it. That puts the ideas and plan of aciton in your head ahead of time.
We can view these requirements in two ways - whatever you need to do just keep from getting a ticket or realizing the benefit that could be had from the devices if you can deploy them and keeping that in mind when you rig them to your boat.
Reminds of the old auto racing days. When they first required roll bars, the racers made these little minimal things that just cleared the body work but obviously would do nothing to protect them in a rollover. Met the letter of the law...