Place a piece of parchment in an 8-inch cake pan. Grease the parchment and sides of cake pan with coconut oil.
In a large bowl, using an electric hand mixer on medium speed, cream the coconut oil and honey until whipped, about 3 minutes. Add the eggs one at a time, beating until combined after each and scraping down the sides and bottom of the bowl as needed. Beat in the vanilla extract.
In a medium bowl, whisk together the sweet rice and oat flours with the baking powder and salt.
With the mixer on low, stir half of the flour mixture into the butter mixture until just combined. Stir in the coconut milk until just combined, then add the rest of the flour, scraping down the sides and bottom of the bowl as needed.
Position a rack in the center of the oven and heat to 350º F.
Now make the nectarines: In a cast iron skillet or large frying pan melt the coconut oil and maple syrup over medium heat. Add the nectarine slices and reduce heat to low, stirring them frequently until slices are soft and slightly caramelized, about 5 minutes. Remove from heat and let cool for a few minutes
Arrange the nectarine slices in the pan in concentric circles, having them slightly overlap each other if you can. Drizzle any remaining liquid from the pan over the fruit.
Spread the batter evenly over the fruit in the pan.
Place the cake in the oven and bake until the top is golden and a toothpick inserted near the center comes out clean, the top is set, and the edges are slightly coming away from the pan, 40-50 minutes. Remove from oven and let cake cool completely in the pan on a rack, then invert onto a serving platter and peel away the parchment. Serve the cake at room temperature.
Cake can be stored, covered, in the fridge for 3 days.