When we first meet Coppy, he's forcing a kid to breathe into a breathalyzer attached to his motorcycle: The bike won't start unless "Coppy" has been alcohol-free for 24 hours, and Coppy clearly has not been dry that long. Tellingly, when the motorcycle successfully starts, he heads straight to "his" bar. (When people, amazed, ask if he owns the establishment, he clarifies: Someone else owns it, "I just drink there.")
Coppy drinks at that bar. Later, when he's shot and asks Rory to find him something to drink, Rory digs up some warm light beer. ("I guess I'll drink a case of warm beer and bleed out," Coppy whines.) But eventually, he runs out of time to drink. And when Coppy unsuccessfully begs someone else to breathe into his breathalyzer, he soon realizes he didn't need their help. (The film suggests this momentary spate of sobriety may become more common for Coppy.)
Other characters also drink. One takes swigs out of a flask during a moment of stress. Several law enforcement officials drink during a tense standoff (involving plenty of bristling weapons).