As someone who has already sent two emails to our hotel regarding what bourbons we want at the bar, I agree with the others who say bring your own. We did this last year and no problem. And others, like they said, do it all the time without incident.
Mega Mart may have it - they will have it if anyone does (vs local Negril shops). But if it's important to you, and you're staying at hotel with bar, ask them if they can order a bottle to have at the bar.
It can take a long time to get someone in once you are there, so I ask them to load up in advance with things I know we will want - like club soda. It's the only thing I drink (well, with vodka in it LOL) - and when the bar runs out, it's hard to find. One year I had people bringing it to me from wherever they went and saw it - was pretty funny.