We enjoy April or May. Christmas winds are well out of the way and the heat of high summer not yet arrived. Not so busy, yet everywhere still open. Works for us, but obviously everyone has their times when they are more able to take vacation.
We have been visiting the BVI for over 15 years now, generally spending a minimum of 14-28 days in the islands per trip, so we do have a little experience! Been in nearly all months for the year, except July-October, but we are still learning!