Beach Club Marketplace (the little store/gift shop there) is actually a grab n go food location, and has a few breakfast items (pastries, some croissant breakfast sandwiches and the like.)...you can get your refillable mug filled there. They're open at 7:00 AM so you can get a quick/light breakfast and your choice of soda or coffee in the AM
If you're just looking for coffee in the AM, your room should have a coffeemaker too...leave a note for the maid to leave extra coffee packets if what is there is not enough for you every day. We're big coffee drinkers and always had housekeeping leave us extra coffee, never been a problem.