Combine flour, sugar, baking powder, baking soda and salt in the bowl of a food processor. Pulse to combine. Add butter; pulse until mixture is the consistency of coarse meal. Add sour cream. Pulse. Add milk, 1 tablespoon at a time, and pulse until dough comes together. Remove from processor; divide dough in half and cover each piece with plastic wrap. Refrigerate 8 hours or overnight.
Preheat oven to 375F.
Place one piece of dough on a floured surface. Shape into a 12-inch log. Roll until dough is a 12 x 5-inch rectangle. Place cherries on dough, pressing them gently into the dough. Fold dough in half lengthwise. Cut dough into triangles and place on a baking sheet lined with parchment paper. Repeat with remaining dough.
Sprinkle tops of scones with coarse sugar. Bake 18 to 20 minutes, until lightly browned.