Coffee Mak on the corner of 30 Av and Calle 11 has good espresso and I think they open at 7. They put too much (i.e., some) cinnamon on their cappuccino, but their real issue is that, at least when I went, they weren't very fast.
Distance-wise you're probably better off at El Coffee Cozumel on Calle 3 Sur just off Melgar next to Pizza Hut if you just want coffee. I suspect that's what's been referred to as "Coffee Bean". They do their own roasting of decent Chiapas beans and pull a respectable shot.
If you want breakfast with your coffee, La Cozumeleña on 10 Av and Calle 3 Sur has great breakfasts and an espresso machine (recently, though, they seem to have been using a Nespresso system) and opens at 7. They're fast enough for a pre-dive breakfast.
Cozazón Contento on 10 Av and Calle 2 Norte is a very pleasant little place run by the former operators of Del Museo. They have a good espresso machine and very nice breakfasts including some great healthy choices. They open at 7 and should allow you to get to the boat in time full of breakfast and espresso.
Panadería Zermatt on 5 Av and Calle 4 Norte has pastries and an espresso machine that, every time I've been there, has been out of operation. They open at 7.
There are others, but those are the only places with which I have personal experience that might meet your criteria.
Personally, I have a source for really impressive beans roasted in Playa del Carmen and make my own espresso at the house, but since you'll never catch me up that early you're on your own.
