Do you mean that you want a tablet that adds carbon dioxide to water to make it sparkling the same way that a reusable soda siphon does by using a cartridge of CO2 gas?
A solid tablet would have to make carbon dioxide from two solid chemicals that react together when wetted. That would typically be an acid substance with carbonate salt, often sodium bicarbonate. Some acids that could be used are citric acid from citrus fruits, ascorbic acid (vitamin C) or tartaric acid. However whatever reaction you used, they always have by products, the things that are left behind from the chemicals that is not CO2.
The only way to add carbon dioxide as a solid without other things would be to drop in a pellet of dry ice, CO2 that is cold enough to freeze solid at -78°C. Could be done but it’s hard to control, there is a danger of cold burns and you can’t stop it evaporating away in a domestic environment as even a freezer is too warm.
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