Recipes for beverages similar to grape Nehi, a grape-flavored soda, can be found on the Saveur and Eating Well websites. These recipes can be made with fresh grapes or with grape juice.
To make grape soda, puree 4 cups of grapes in a blender and strain the juice in a sieve. Add 2 tablespoons of honey and 2 tablespoons of lemon to flavor, and mix with 2 cups of seltzer.
Alternatively, use champagne yeast for carbonation. Simmer 2 3/4 cups of grape juice, 1/4 cup of sugar and 2 3/4 cups water in a pan for 30 minutes. Add 1/8 teaspoon champagne yeast and let the mixture sit for a day. Bottle the mixture and let it sit at room temperature for a day, and refrigerate for two days before opening.