In a food processor or blender, puree the cherries until smooth. Strain the liquid with a mesh strainer. Set aside.

In a small saucepan, combine the sugar and water. Bring to a boil over medium high heat, stirring to dissolve the sugar. Remove from heat and combine with the cherry juice and lime juice. Chill mixture completely.

In a 11x13 inch dish, combine the cherry and lime mixture with the club soda. Increase or decrease the amount of club soda to your taste. Place in the freezer. After 1 hour, use a fork to break up all frozen parts. Repeat this process every hour until all of the mixture is frozen, about 4 hours.