Carbonated water is not the way to do that. It's expensive, acidic, and inefficient, and totally inappropriate for use in flower (no misting flowering plants!!!)
Coal?! No no no that is just fossilized hydrocarbons; skip the million years of fossilization and water with sugar water instead. KISS.
Use CO2 gas if you have all your other environmental factors tweaked to perfection already. Remember that you can add all the carbon you want and not see benefits if other aspects of your grow are not optimized.