Drain cherries and set on paper towel to dry
In a medium bowl, combine butter and corn syrup until smooth.
Stir in powdered sugar and knead to form a dough. Chill to stiffen if necessary.
Wrap each cherry in about 1 teaspoon of dough.
Place wrapped cherries on a cookie sheet and chill until firm.
In a microwave-safe bowl melt chocolate chips with oil for about 20 seconds at a time (stirring each time) until chocolate is just melted and completely smooth. Dip each cherry in by its stem.
Place dipped cherries on wax paper-lined sheets. Allow chocolate to dry/harden.
When chocolate is no longer shiny, place chocolate covered cherries in an air-tight container (like a large Tupperware or Rubbermaid container). Store in a cool place for TWO WEEKS (yes, it is a long time, but patience, I promise they taste best if you wait until the fondant softens)
After two weeks, cherries can be served or gifted in candy wrappers, gift bags, or boxes.