Chill the pineapple juice and soda until very cold. Soften sherbet for 5 minutes on the counter.
Pour corn syrup on a small plate and red sanding sugar on another. Dip glass rims in syrup, then coat with sugar. Set aside.
Add scoops of lime sherbet to a large punch bowl.
Pour in pineapple juice and vanilla extract, then gently stir to start melting the sherbet.
Slowly add the lemon-lime soda down the side of the bowl to keep the fizz. Stir lightly.
Tint with a few drops of green food coloring if desired. Add ice, lime slices, and cherries.
Ladle into the sugared glasses and serve right away while frothy.