Hey, Batman. I saw your post, and I think I have an idea for you.
Cetaceans. In spite of the fact that they live in water, creatures such dolphins and whales rely a lot on sound production much more than their other senses because water dulls those perceptions. Dolphins use high-pitched clicks for navigation, and whales use songs and other vocalizations for communication with others. The key to these is to actually be able to produce sound underwater, and they have the best mechanisms for the job.
You're right in that one cannot just pick up an object and beat on it like a drum; water is far too dense for both the effort to strike an instrument and allow that instrument to vibrate in a fashion that allows sound production. So, cetaceans have air-based mechanisms that they use to produce sounds instead. The vocal tracts of baleen whales are enclosed systems of sacs and a larynx connected to their lungs. They simply press air from their lungs to what is called a laryngeal sac, passing the air through vocal folds in the larynx. And since whales are so big, we're talking about a lot of pressure creating vibrations on those vocal folds, which then resonate out of the whale as sound. Dolphins, porpoises, and toothed whales have a different structure, wherein sound is produced just inside the blowhole by passing air from the lower part of the nasal complex into a vestibular sac, where the air can then be returned to the lower nasal complex or expelled through the blowhole. This air, in passing, goes through what are known as "phonic lips", which is how these animals produce their clicks and whistles.
In either system, air is contained within the body and produced without actually needing to expel it (you can even do this, just keep your mouth closed, hold your nose shut, and try to hum or groan; as long as you can make your vocal cords vibrate, you can still produce sound). So, if you want an instrument that functions underwater, one mechanism would be an instrument that contains air in a closed system. A pair of sacs or other flexible containers could be joined together by a narrow structure containing small, vibrating elements that, when air is forced through at sufficient pressure, can overcome the deafening properties of the water outside the instrument and produce an audible sound. The sound, like any other instrument, could be changed by the use of a physical mechanism, such as a key like a piano, to halt the vibration of a selected vibrating element. In the process of playing, as one sac is squeezed, the other sac inflates in reception of the air contained within. Now, here, the sound may be returned by squeezing the second sac, or this second sac has an elastic property which causes the air to flow back to the first sac without input from the musician. In order to create this instrument, the builder would have to capture air from the surface into a sac and connect it to the instrument without allowing any water inside.
What do you think?