No place at the airport to pick up a cell phone. If you have a private driver, have him stop on the way to Negril and pick one up. Numerous places sell them. Mega Mart in Mo Bay comes to mind.
If taking a tour bus, there are several outlets in Negril. Digicel and Lime both have outlets in "downtown" Negril. A taxi ride may be necessary, depending on where you're staying.