Hi. In St. Maartin, we went to Divi Little Bay resort (wonderful). They have jet skis available for a fee. My husband rode them all day(you have to pay for an hour each time). I don't remember the cost but I want to say it was between $30-50.
There is also jet ski rentals in St Marteen right on the main beach area where the ships dock. It was over 2 yrs ago when I was there... but rentals were about $50 for an hour. There is a shuttle/water taxi that will take you from the cruise ship dock to a small dock right in the center of town. There are (or were) jet ski and other water sport rentals right on the beach just to the left of the pier. We rented them for about 2 hours between 10 people and had a blast.
In Key West.... there are jet ski rentals also available right in Mallory Square... which is the area where the cruise ships dock. Not sure of the rental prices there....
As far as Cozumel.... try going to cozumelinsider.com. On that site there is a listing of activities and the beaches on the island. It will tell you what beaches offer jet ski rentals.
Coki Beach at St. Thomas. Prices were reasonable and when you were done Jet Skiing the snorkel was awesome right off the beach. We even saw a shark. Don't book this through a cruise ship though. Just take a cab to Coki. Beach is free. They serve food and drinks right on the beach. You can use the server for Coronas for 3 bucks each or walk 50 ft to the vendor and get em for 2 bucks. This was one of the best days of my life. They also have SNUBA diving there and everything. Very uncrowded and beautiful. Good Luck