Combine the pineapple juice with the corn starch to make a slurry, and set aside (this will be used to thicken the sauce later).
Stem, pit and slice the cherries in half. Extract the cherry juice by combining the prepared cherries with 3 tablespoons of water in a small saucepan.
Simmer over low heat until the fruit softens. Gently mash the cherries with a potato masher, and continue simmering until the juices are released.
Strain and discard the solids. Measure out 1/8 cup of cherry juice (add more water if needed).
Add the cherry juice, ketchup, vinegar, and soy sauce to the saucepan. Heat and stir over medium heat until combined.
Add the sugar and continue simmering over medium heat while stirring. Taste and add more sugar if you want a sweeter flavor.
Once the sugar is dissolved, stir the pineapple juice slurry, and add it to the saucepan.
While stirring, bring the saucepan to a boil over medium-high heat.
Reduce the heat to low and simmer until the sauce thickens, about 5 minutes.
Remove the pan from the heat and allow the sweet and sour sauce to cool. Makes about 2 cups.
Use immediately, or store the refrigerator for up to a week, or freeze for up to 4 months.