As JD says, there is a small store right there in Royal Palm that has pastries and I have no idea whether they sell coffee there or not. The breakfast at the Yacht Club is very good and they have American coffee there. Zee Best is pretty close and they MAY have American coffee there, but frankly I've never eaten there. Not walking distance for me personally, because I'm lazy, but really close in the car is the Hideaway at Lavista. They have good full American breakfast there.

As the others said, I personally would just make coffee in the room and enjoy your balcony there at RP, but it's your vacation--do what you like!