The cheapest way is to bring it with you next time you visit. The only other economical way is to have a barrel shipped by freighter, at least for us that live near the east coast. But that only makes sense if you need to ship a lot of stuff. Retrieving the barrel once it arrives can be a hassle, or so I hear.
The lack of shipping options really amazed me when I looked into it. You would think in this day of global commerce, where I can routinely get packages shipped from China at little cost, that we could get small packages shipped to Jamaica without it costing more then the contents.
I often thought about the idea of starting an online retailer based in Jamaica that would accept online orders from around the world for delivery within Jamaica.