My T-Mobile phone has worked throughout the Caribbean over the past couple of years. It works well in The Grenadines, Carriacou, and Grenada as the OP asked - but the data is 3G at best, but functional.

The only island I had problems on was Antigua. For the most part, it did not connect to their partner networks there, although the phone could see them. On occasion, I did get a connection. This problem persisted for the month I was there - I'm not sure about the issue.

I did have some issues with receiving texts in the French West Indies. I could not get a text sent from my broker, but I could get others.