Preheat oven to 400 degrees. In a small bowl, combine 2 tablespoons sugar and the cinnamon. Lay 1 phyllo sheet on a baking tray (keep remaining pieces covered with a damp kitchen towel) and lightly brush entire surface with oil. Sprinkle with 1 teaspoon cinnamon sugar. Repeat with remaining phyllo sheets. Arrange cherries on top. Sprinkle with remaining sugar.
Bake until crisp and golden brown, 15 to 17 minutes. Cut into squares.