Position an oven rack in the middle of the oven and preheat to 350 degrees F.
In a large bowl, combine the flours, quick oats, flax seed, wheat germ, baking soda, cinnamon, salt and baking powder.
In a stand mixer, cream together the butter, coconut oil, brown sugar, honey and peanut butter until creamy and well mixed, about 4 minutes, scraping down the bowl halfway through. Add the egg and mix until incorporated. Add the flour mixture and mix just until incorporated. Fold in the granola, cherries and coconut.
In a 9 by 13-inch baking pan, place a piece of parchment across the bottom (it will extend over the long sides, but not the ends). Spray with nonstick spray. Add the dough to the pan and cover with plastic wrap. Using your hands, gently press the dough out into the pan until evenly spread. Place the pan on the middle rack and bake until the edges are starting to brown lightly and a toothpick comes out clean, 35 to 40 minutes. Remove from the oven and cool in the pan for 15 to 20 minutes. Then gently lift the parchment out onto a cooling rack and cool completely; it will firm up as it cools, but crumble if you move it too soon. Once completely cool, move to a cutting board and cut into bars with a bench scraper or large knife, about 3 by 1-inch each.