99% of the time your insurance, be it travel insurance you bought, something that comes with a credit card or your own car insurance at home, will NOT cover you renting a car in Jamaica.
If you don't have the deposit then you can rent from Island - they offer a full insurance rate that covers you for all but about $250. Higher per-day price but no liability at ALL, thus no deposit required (beyond $250 in case you return the car late or whatever). That no-liability coverage costs $27 a day plus the rental.
However, they will charge you a pickup/dropoff fee for getting the car in and returning it in Negril. That's $40 each way. So you'll still pay like $150 for one car for one day. Plus gas. I'm not sure a private driver would charge much more than that, might even be cheaper.
If you get the car in MoBay and return it there also, then it's pretty reasonable - $70ish for 24 hours with the insurance.
(edited to add, OneStop seems to be quoting Island's rates so they might be able to save the pickup/dropoff fee - maybe ask them directly).