Preheat oven to 450 degrees. Spray 2 (6 count) doughnut pans with cooking spray.
In a mixing bowl, whisk together the flour, cocoa powder, baking powder, baking soda and salt. In another mixing bowl, whisk together the sugar, eggs, oil, rice milk, vanilla and coffee. Add the wet ingredients to the dry ingredients and whisk to combine. Spoon the batter into the doughnut pans, filling each form about ¾ full. Bake for 7 – 9 minutes or until the doughnuts spring back when lightly touched and a toothpick inserted into a doughnut comes out clean. Let cool in the pan for 2 -3 minutes, then remove to a baking rack to finish cooling completely. Can be made a day or two ahead.
Place the graham style crackers in a small plastic bag and crush them with a rolling pin until you have some larger pieces (about ¼ inch) and some crumbs. Place on a small plate.
With a knife or small offset spatula, spread about 1 tablespoon of the Toasted Marshmallow Crème on the top of each doughnut, then dip into the crushed graham style crackers.