What is the correct pronunciation of "Caribbean"?

Judy Garland
Mack The Black ('The Pirate', 1948)

"There's a pirate, known to fame
Black Macocco was the Pirate's name
In his day, the tops was he
Round the CaribBEan or CaRIBbean Sea"

So unless you disagree with Judy Garland, either's possible. Case closed, I think.