Do you need a passport for Southern Caribbean?

Yes, unless you are a US citizen and this is a closed-loop cruise. From the getyouhome.gov website: U.S. citizens who board a cruise ship at a port within the United States, travel only within the Western Hemisphere, and return to the same U.S. port on the same ship may present a government issued photo identification, along with proof of citizenship (an original or copy of his or her birth certificate, a Consular report of Birth Abroad, or a Certificate of Naturalization). Please be aware that you may still be required to present a passport to enter the foreign countries your cruise ship is visiting. Check with your cruise line to ensure you have the appropriate documents. Note that Southern Caribbean cruises often start and end in San Juan, Puerto Rico which is part of the United States.