In a large pitcher add the coffee, coconut and 3 cups water. Stir and refrigerate, stirring every few hours, at least 8 hours or up to overnight.
Wet a paper towel or use a coffee filter placed in a fine mesh sieve over a pitcher. Pour the cold-brewed coffee into the lined sieve and allow it to drip into the pitcher beneath. Push through gently at the end to get the last bit of coffee. Add the evaporated milk to taste, then sweeten if desired and serve over ice.