Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
"The only exception that I know of is the Alaska Airlines Visa which gives 25,000 points upon approval, however, they wouldn't be an option to the Caribbean."
Why not? AS miles are redeemable for travel on lots of other airlines, including AA and DL. (Not sure how many AS miles are required though for an award to the Caribbean.)
Would the Barclay Arrival+ card work for the OP?