Hi Alix,
Yes, as Susan suggests, a photo would be helpful.
Unless there is danger of more of the coral being damaged around the area of the previous break, my inclination would be to keep the piece separate for now instead of trying to glue it back in place. I will pass along your inquiry to a specialist in Natural History conservation for any other suggestions they may have.
Selecting a suitable adhesive for repairs such as these can be tricky because you would want to consider the coral’s sensitivity, the strength of the join you need, and the ageing properties of the adhesive, among many other factors, so it is hard to recommend a particular product without having more information or seeing the object.