(I found some wonderful pieces of coral on the beach in Bimini, Bahamas. They were still spongey and very wet, so they must have been broken in the surf that day. They've been sitting on my patio for a week, but they are still a bit soft. How do I make them harden and turn white? They're a greyish color right now)
There are two general types of corals – soft corals, where the matrix material is tough but flexible (a sea fan is an example); and hard or stony corals where the matrix is calcified, inflexible, and stone-like. If your specimen is flexible, it is not a hard coral and there is no way to make it hard. If it has a hard, stony core but is covered by a thin soft layer, these are the polyps and should be removed by soaking in 10% Chlorox for a few hours, followed by a fresh water rinse. This will also whiten the hard parts. However, if your specimen is a soft coral, or perhaps a sponge of some sort, soaking in bleach will completely destroy it.
(Answer by M. Paul Monfils via the Forum)