If you will be around for as long as a whole Monday to Friday week at a time, you may find that there are indeed camps where he could be a counselor (unpaid--don't expect pay for camp counseling at his age).
Not all camps are all summer long, so have you looked for one- or two-week camps that might need counselors? Some camps do expect teen counselors to be signed up already by this time of year and to do some training in advance (our Girl Scout camp's training involves about two evening meetings in spring and a full-day Saturday the week before the camp for instance). But don't rule out camps just because you're traveling much of the time. You do need to look ASAP if you think camp counseling is an option. Involve him in the search!
You mention that no one will hire a kid under 16 in your area but think outside the box of employment. Some volunteer organizations will accept younger teen volunteers:
Your local library may have a "summer library page" program where kids act as pages, doing everything from signing kids up for the summer reading programs to shelving books to helping run events or used book sales. This is unpaid but looks great on a "resume" when high school clubs ask you what you've done for community service.
Do you have a church, synagogue or other place of worship? Does it need the grass cut, or painting done somewhere, etc.? Does it run a summer program of any kind, vacation Bible school or summer Hebrew school or whatever? Those programs actually usually like the idea of teen boys helping because they want good role models for the younger boys who attend.
In our area, there are web sites with tons of volunteer opportunity listings, and you could look online for those open to kids his age. If one looks really interesting to him, and it says it's for older teens, have him call anyway and express how interested he is -- they might be short on volunteers and find a place for him.
See if your town or county government has volunteer programs in summer for teens. The parks department in my hometown did that.
Do you have needs around your own home? This summer, my 13-year-old will be earning money from me doing some big tasks that are outside the usual week to week chores. The pantry needs a huge clear-out, the linen closet needs total clear-out and repaint inside -- lots more. Can you work out a list of chores that are beyond the usual and are you willing to pay him pretty well for them?
He could also start a business over the summer, mowing lawns or (if everyone in your area has a lawn service, which some folks just do) washing cars. He can spend some time at the start making flyers, e-mailing neighbors, circulating information. Good experience.
Is there a specific reason you say you need to keep him "out of trouble" or do you just mean that as an expression--?