I know. This is work and not fun. By the time you are finished looking at all the travel websites, airline sites, aggregators, etc., you will be ready to tear your hair out. But it can save you a significant amount of money. There really is no way around it.
One place to start is to find out what airline has the most service to the island you want to travel to. The official tourism website of the island usually lists which airline services that country.
Many times this will be American because they pretty much dominate the Caribbean routes. Others, such as Delta and US Air, have been making inroads though. Whichever airline it is, go directly to that airlines website. They often run specials and often guarantee the lowest prices from their website so it's a good bet for cheap airfare.
Compare that price to what the travel sites and aggregators are offering (cheaptickets.com, Orbitz, Travelocity, Expedia, Kayak, etc.). One site I really like and use all the time is Tripadvisor
Kayak also gives you the price history of your ticket so you can see what the price has been doing.
I also subscribe to the newsletter for Airfarewatchdog.com. It gives you fares from the airport of your choice and several alternate airports, depending on where you live. It also tells you availability of seats so you might actually have a chance of booking one.
Travel in the Offseason.
Even if you go a week before high season, you can usually find good deals. High season for the Caribbean is mid-December through mid-April and is the hardest time to find cheap airfare. You will be taking a little more of a risk with weather, though, so keep this in mind.
Purchase Tickets Early.
For international travel, you can usually get the best prices if you purchase your tickets 3-6 months ahead. This is especially true if you are traveling during peak season.
Frequent Flyer Miles
An obvious one, I know. But here is one tip for actually being able to get a seat on some popular routes. Many times frequent flyer seats are gone as soon as they come out.
Find out when the airline first opened the seats up to FF (typically 6-9 months before a flight). An airline will only hold a reservation for so long before it automatically cancels. Find out what the policy is for your airline. Then call at midnight, or whenever the FF department opens, on the cancellation day to see if any seats have become available.
This applies to both airports and travel dates. Sometimes you can find cheaper fares if you are willing to travel out of alternate airports. Many search engines have this option when you are searching for fares.
Flexibility in your dates, though, will probably save you the most money and make it easier to find cheap airfare. Sometimes if you just switch by a week, there can be a significant price difference. Even during the same week, the price can vary significantly. Mid-week departures are usually less than flights leaving on Friday and Saturday.
Request a Refund.
If your fare goes down after you have purchased a ticket, many airlines will refund you the difference. It is not publicized and you have to know to ask for it. If they don't refund the difference, they might offer you a credit toward you next flight. So keep checking the prices even after you have your ticket in hand.
A few years ago, we received a credit from American Airlines. It was in the neighborhood of $100 per ticket. Although they didn't make it easy for us to collect (we had to physically go to a ticket office; we were living in NYC at the time), it was worth the effort.
So do your research, search around and you too should find a cheap airfare (or, at least, a cheaper one) for that next scuba dive vacation.