Yes I have been riding in the caribbean twice. Lucky Stables in St maarten - - went on my own with their guide and it was fantastic - it lasted about 2 hours and included the horse going wading into the sea - well worth getting my breeches and boots soaked for( I knew in advance so wore old gear) cant rememeber exactly how much it cost, somewhwere between US$60-90. I had to make my own way there and back by taxi but it wasn't that far from the docks (20-30 minutes). Also went riding on St Lucia think the stables were called Atlantic Shores or something like that. Again I went out on my own, so the ride was tailored to my riding level (intermediate to advanced). Guide and horses were both great. the views over quiet bays and up on high cliffs were stunning. Also they pick you up from the cruise terminal and bring you back (and it's included in the price of the ride) Transfer time to the stables was about an hour each way. Cost about the same as the other in St Maarten. From memory both stables had weight restrictions of 180 pounds (It's quite normal in most parts of the world) Don't know if this weight restriction would be a problem or not for you. You could try enquiring if they have any horses capable of carrying heavier weights. cant say i noticed any at either place - most looked like thoroughbred cross types. Guess it will depend if you are only slightly over and whether you are an experienced rider or not.
The ships do shore excusrsions sometimes but I preferred making my own arrangements as i didn't want to end up with a huge group of people who had never ridden before.
If you are not going to these islands, then you could try either the BHS website for recommended stables overseas or alsothe caribbean Horse riding site (can't rememebr the exact name but if you do horse riding + Caribbean in google, it should come up).
try this site for the answers.