Cathy, I would use simple dishwashing detergent and warm water. There
is no need for anything stronger unless there is a lot of hair spray
or water oils on it. If the coral is completely natural and there is
no dye involved you may want to use some alcohol and gently rub it.
If there is dye present, be prepared to loose some of the color.
Cheers from Don at the Charles Belle Studio in SOFL where simple
elegance IS find jewelry! @coralnut