Would carbonated water be a good substitute for two eggs in this cherry loaf recipe?
It would be useful to see the whole recipe, but the answer is probably no. Egg whites are protein and water, and yolks are fat, protein, and water, and each contributes important things to cakes. There is complicated chemistry going on, and you can't just eliminate the eggs from a recipe like this. Carbonation does nothing. However, if your recipe calls for, e.g., whipping the whites to create a stable foam, you could replace this with whipped aquafaba. There are other similar vegan substitutions that could be made depending on how your recipe is using the egg.