In most Caribbean ports there are outlets for 3 chains that my wife seems to favor. They would be Diamonds International, Columbian Emeralds , and Little Switzerland.
Do your homework before you go shopping in the Caribbean. Know how much the jewelry you want to buy would cost in the US. St Thomas has the most stores, followed
closely by St Martin. There is however good shopping in most ports.
Two things to keep in mind (after you've done your homework in the States). Customs
allowance for items purchased in St. Thomas is double that of any other port(as this is a US protectorate) and loose stones have no duty no matter how much you pay for them. They are essentially a rock for duty purposes. I cannot stress enough doing your homework before you shop in the islands. Know what the same item costs at a reputable outlet in the US and be sure you are comparing similar size , cut and clarity, etc.
Good luck and have fun shopping.
I have never bought Diamonds in the caribbean but I have bought gold in both mexico and St. Thomas. Check the price of gold before you leave but you usually if you shop around you can get gold for $9-$11 a gram that is what we paid for 14K. I knew exactly what I was looking for and I will tell it was not easy I went shop to shop but I found it.