I'm not sure about Baily's but they did have the fixings for mimosas at breakfast in the Palms. Try the rum cream instead of Baily's. It's very similar to Baily's except it uses rum instead of whisky. It comes in different flavors too.
They had jerk chicken at the Cabana Grill every day.
I too enjoy my rum cream with coffee in the morning. My suggestions, ask the bartender for a small cup of either bailey's or rum cream before the beach bar closes. They can put it in a small cup. Put it in your refrigerator, then order your continental breakfast (coffee) for the morning - bingo. Another thing you can do is buy a bottle of Bailey's at the airport and bring it with you. Either way, it'll be good and work out for you. Enjoy. They serve mimosa's at the Palms in the mornings too!
The Palms has a mimosa and Bloody Mary set-up for breakfast. However, the bars don't open until 10:00, so if you are looking for Baileys in your coffee before that, you are out of luck. However, a suggestion would be to buy some Rum Cream at any of the stores along the beach (also available at the CSA gift shop) and use that in your coffee in the morning. A much better choice for Jamaica!