Stir until the sugar is dissolved (or add it while the coffee is still warm and then chill). Pour the chilled coffee mixture into a pan that can go in your freezer.
Set the timer for 30 minutes or so and stir the mixture. Keep setting your timer and stirring until it's frozen but broken up into small shard-like pieces. If you have leftovers, they'll freeze solid but you can scrape them with a fork to break them up again into pieces.