Your best bet is to run a search of universities with nautical archaeology programs (there's very few in fact). From there, see what sorts of "digs" they have ongoing. Underwater archaeology is far more restrictive than the on-land type; as such there are very few field activities taking place throughout the world... like two orders of magnitude less.
Unless you're a professional, it'll be very hard to participate in ANY underwater archaeology. Spaces are highly limited and experience is almost always required. I don't mean to poo-poo you here, but this is the way these things go down. Having someone on the "inside" refer you is the single biggest plus, like most endeavors.
I would seek out any local programs, if there are any, and talk to a graduate student or faculty member. You never know, sometimes great opportunities are offered! Our own department at Texas A&M is first-rate, and they've used volunteers extensively in the past.