I've just got back from Barbados. Most companies deliver the car to your hotel and will collect from the hotel when you have finished with the car. You might consider arranging this and just hopping in a cab from the airport to your accommodation ?
We rented from Fat Jacks car rental, they were pleasant and easy to deal with. The car was a bit of a clunker though (a moke). I would advise you against a moke, as it wasn't the best car for some of the poorly maintained back roads ! If I were renting again I'd go for a 4WD.
Have a great holiday