Dive with Martin is located at the International pier right as you're exiting the dock. You can also use their gear with no added charge if you like. Stayed at a nearby resort last month. Looks like most Carnival and Royal Caribbean ships docked here (there are 3 piers in Cozumel). Their boats leave at 7:30 and 12:30. As noted before, if you leave from a Fl port, that would be an hour later by ships time.
I've been diving in Cozumel twice on Cruises. Both times I had no time to do anything else after taking a taxi to the dive op, waiting for other people to show up, and then getting back to the ship, so timing is important if you'd like to do anything else while you are there.
Good luck with whatever you do!