My experience on a cruise is that the odds are none of them will stamp the passports. If you're flying into one of the islands to catch a cruise, maybe? And sometimes if you try real hard you might be able to find the office that will stamp your passport for you if you really want to, but even that's going to be something of a long shot. I've had one or two cruises where they held my passport, but even for those, not sure they actually got stamped. (And it's been so long, I honestly don't remember which cruises those were that they did that - part of me wants to say that it was the Manaus to Ft Lauderdale, and maybe it was French Guyana (spelling wrong probably) that wanted teh ship to hold them, and that's not even the caribbean. But unless you're starting or ending in one, most of these countries aren't doing physical checks of your passports these days. (I'm sure there's an exception out there, just to prove me wrong.)