Hey so I did a test run myself with some instant coffee and I managed to get it to carbonate.
Here are my steps,
Step 0: Boil water and let cool or used distilled water
Step 1: Mix instant coffee and water into fermenting vessel, about one tablespoon of instant coffee per cup of water
Step 2: Allow the beverage to ferment for at least 3 days
Step 3: Refrigerate just before your desired carbonation is reached
Step 4: Profit
I find that the carbonation is incredibly slow the first day, and the bubbles are kind of foamier compared to a ginger beer. I added some vanilla bean and cinnamon to mine for some complexity and they come through in the resulting drink.