Don't do it!! We have been to Jamaica four times and would NEVER consider driving there. The drivers are very aggressive and seem to follow a system of "rules" we don't understand. Seriously - if you value your life - take a cab.
Generally speaking it's not advised to rent a car and go on your own. A couple reasons for this:
They drive on the left side of the road. This not only makes it more difficult just to drive safely but you could also accidentally make or be forced to make a wrong turn and end up in an area you shouldn't be in. Jamaica is generally considered safe for travel but just like many parts of the U.S. there are places you just shouldn't go.
The general rules of the road are a bit different and maybe even unclear as you will notice immediately during your trip to the resort.
Getting a driver isn't hard and you'll enjoy the trip much more if you can sit back and relax. Ask at the hotel desk and someone ought to be able to set you up. We haven't been to Couple's before but been to Jamaica 15 times and the resort we used to stay at would get you a driver through the desk. You just told them how long you wanted to be gone and they'd arrange it. You can even negotiate a little with the driver on price.
Leave the driving to the Jamaicans. I have no problem driving in downtown Chicago, but wouldn't even consider driving in Jamaica...and not because they drive on the left side of the road. The drivers there are nuts, there are tons of pedestrians and animals walking on the roadways and the roads are narrow and have a lot of blind curves. Hire a driver!