before 9/11 after you went through customs and outside you could circle back around to the departure area and go to the duty free shops but now you have to go through a layer of security to get to the shops
Assuming you are departing from the U.S., most gateway airports have duty free shops where you can buy cigarettes, booze, and other items duty free. For example, Charlotte has a duty free shop in the food court area between B and C terminals. We buy our duty free items, show them our international boarding pass (you can only shop there if you are boarding an international flight), and they deliver the goods to us at the gate. Philadelphia also has a duty free shop in the A terminal.
Buy the cigs. you will need IN Jamaica at the duty free in your departure airport. They will be given to you as you board the plane to leave the US. Jamaican Customs "says" you are allowed to bring one carton per person into Jamaica. Mr2cool buys the 5 carton box when he leaves the US and ONLY once were we stopped at customs. The solution was to take one carton to the resort and leave the remaining 4 at customs to claim when we left the country. No problem either way.