Coral Reef and Volcanic Islands
I just came upon this paper by Tomascik et al. (1996). It does not answer directly your question, but I found it sufficiently relevant to post it here anyway. It's a study of coral colonization after emplacement of a lava flow. They found that only five years after emplacement of an andesitic lava flow from Gunung Api in 1988, large parts of this new coastline was already covered by coral. They mention a previous study (Grigg and Maragos 1974) on Hawaii where it took 20-50 years for coral to colonize a submerged lava flow.

Of course, in those cases the coral could come from nearby reefs, while in the case of a new island it has to come from further away. So those fast colonization timescales are not directly applicable to your question.