Caribbean countries have strict gun laws and for the most part are corrupt. Be prepared to fork out bribe money. Generally, these countries also feel you having a gun is a threat to their economy. Why? Because if people knew how to defend themselves, it would take away from the profits of the many security firms that operate in those countries. Third world countries in general, rather have you hire a full time armed security guard then for you to perform your own security. Many of the security firms have some type of a connection with government directly. Basically, they feel that somehow, they want to profit from protecting you and also that with the low wages in those countries, why not be able to support someone and his family with a security job.
Most likely the security guard will be incompetent, undertrained and who can vouch for how trustworthy? The rigorous criteria we may have in our own country is non-existant there. They just take some guy from streets, put a uniform on him, give him some basic firearm lessons and now he is the guy to defend you and your family. There was a report about two Canadian tourists killed in Dominican Republic after the thieves bribed the guard of their hotel, who assisted in aiding them to their victims.
I was reading that non-citizens have hard time getting guns in those countries.
But as I say, connections are everything in these type of countries. So, if it is somehow profitable for some government agent to arm yourself, then it may be worth his while to help you. Third world countries are miserable when it comes to deal with bureaucracy. Don't feel shy or ashamed to ask if there is something you can do for so and so to speed things up.. Its just how things work there.