Stir together butter and corn syrup in a medium bowl until smooth.
Mix in confectioners' sugar and knead to form a dough.
Wrap each cherry in about 1 teaspoon dough. Chill in the refrigerator until firm.
Melt chocolate discs in a heavy saucepan over low heat, or microwave at 50% power for 30 second intervals, staring until smooth.
Holding onto the stem, dip each cherry into coating and place on waxed paper-lined sheet trays. Chill in the refrigerator until coating is set. Store in an airtight container in a cool place.