You all know I'm new and have little experience, but Mike at WSSI told me all woods will stabilize. We were talking about Thuya. You may want to ask him if the following advice also applies to cocobolo.
"All wood will process. The Thuya will weap its natural oils out after I'm done though. What is needed with this is patience. You'll have to expose the thuya to a window sill for the sun to warm it and the oil will weep out alittle faster, a couple times a week you will want to wipe the oil off with acetone or finger nail polish remover or sand it off if you have enough stock to do so. This may have to be repeated for a 2-6 weeks depending on the amount of oil the wood has. When it is done it buff and looks great. "
If you do try it, let us know how it works.
Rob!