Not sure if there is currently anything in Coral Bay, but if you are going to any of the beaches closer to Cruz Bay for the day, drive into town and pick up sandwiches from Baked in the Sun (my favorite) or Deli Grotto and then head back to the beach. Bagels or breakfast sandwiches from Baked in the Sun are soooo good!
Donkey Diner has a breakfast burrito, but you would probably not take it to the beach. Knife and fork affair. Don't forget to try Sam and Jack's deli too. They roast all their deli meat in house which has NO preservatives and in my opinion far exceed the competition for sandwiches.
Donkey Diner does an egg sandwich and you can add a meat option. Also, sometimes on their specials board they have breakfast burritos on the smaller side(eat out of hand). Laura
You must be the change you want to see in the world