Tea and coffee as a total substitute for water is not a good idea, your kidneys are working especially hard on such a low carb diet so they need water to flush the system. Could you compromise? Every time you have a cup of coffee, have a small glass of water just before? That way, bit by bit, you might be able to at least have half of your fluid intake in the day in the form of water.
Or how about peppermint tea? Settles the stomach too. Or green tea?