I wouldn't even try the unaccompanied minor route. Probably just as cheap for you to go along.

If you simply want to give him the experience of flying, you could do a one-way flight in the morning to Boston for about $60 (I checked Saturdays in September) and then take MegaBus or a similar service back to NYC. Those tickets can often be had for $10 or less. Public transit from the airport to the bus station in Boston is cheap and frequent. That would bring down the cost of the excursion significantly and it's still an easy day trip. The flight would be short but would otherwise be the genuine article.