The dune buggy-like vehicles you saw were probably the Island Cruisers that used to be available for rent, right on Norman Manley Blvd. Unfortunately, they went out of business a couple years ago.

Another option is to rent a car through Budget Rental at Sangsters. They offer Suzuki Jimnys, which are similar to the Sidekicks that used to be available in North America. Just a word of caution - I rented a Jimny in Virgin Gorda several years ago and the thing felt like it had 2-cylinder engine. I was being overtaken by every local that approached me (which at least forced me to drive safely).