The bars at Park Royal Cozumel offer a great variety of hard and soft liquor, as well as imported varieties of America's favorites. Overall, Corona is their big hit (because it is straight from Mexico). At Park Royal, my favorite addiction was an "Okie Dokie". (Can't mention ingredients because I would give away one the bartenders little secrets.) If you get down there, just mention it. You'll love it.
In addition, the downtown district of Cozumel offers great specials, like two-for-ones. Americans drink free (tips reccomended), and first one to "walk the plank" drinks free the next night. All these bars are intended for a relaxing and enjoyable time. The atmosphere is great. Go and enjoy it. It is an unforgettable experience.
Oh yeah--one more key piece of information for you. Don't worry about driving. Taxis are quick, and you don't pay by 1/9 of a mile. It is five dollars for virtually anywhere you want to go. Can't beat that deal.