Dear Alex
Zanzibar in April is usually rainy however, lately the seasons have changed dramatically hence this year the rains may delay and arrive end of April, beginning of May. Also, it depends where in Zanzibar you are - The Northern tip i.e. Nungwi peninsula usually sees rain in the early mornings and late evenings giving the guests some time to enjoy the in between. On some days, it can remain cloudy for longer, but it is never 24/7 and not gloomy-you can still find alot of things to do on such days.
BUT - in the end, it is nature and you never know what happens next - I was giving you my personal insight after knowing the island so well over the years.
Hope this helps,
Warm regards,
Vinay Sapra
On: 31 January 2012