The Collaborative International Dictionary of English v.0.48:

Corallite \Cor"al*lite\, n. [L. corallum coral.]
   1. (Min.) A mineral substance or petrifaction, in the form of
      coral.
      [1913 Webster]

   2. (Zool.) One of the individual members of a compound coral;
      or that part formed by a single coral animal. [Written
      also corallet.]
      [1913 Webster]