Preheat the oven to 350 degrees.
In a medium bowl combine the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl beat together the brown sugar, eggs, sour cream, and applesauce. Mix well then stir in the vegetable oil and vanilla.
Add half the flour mixture to the brown sugar mixture and mix well. Add the milk and mix until combined. Add remaining flour and mix well.
Fold in the cherries. Pour into a bread pan sprayed with cooking spray.
In a small bowl combine all the ingredients for the streusel. Crumble over the top of the bread.
Bake for 55-60 minutes or until a toothpick inserted into the center comes out clean.