Please see my note on the pronunciation page for "Caribbean" (be sure to type a capital C). And for more detailed information, read the entry on this word in my Big Book of Beastly Mispronunciations (p. 78-9).
I do not understand the allowance of two ways to pronounce this word. It is a compound word made up of two words unto themselves and should only be pronounced by saying the two words as one. Carib Bean. It should NOT be pronounced as if it only had one B. caribean. (cah rib ean)