The ride name is like Data on Star Trek. It's a proper name and thus has one correct pronounciation. And official material from Disney AFAIK pronounces it kar-i-BEE-uhn. So that's what I say when talking about the ride.
That said, when referring to the body of water in real life (like if I'm going on a cruise or such), I say kah-RI-bee-uhn
While both pronunciations are acceptable, in general, when used as a noun, the BEE is accented (as in Pirates of the Caribbean), but, when used as an adjective, the RIB is accented (the Caribbean Sea).