Preheat the oven to 350 degrees. Spray two 9 inch cake pans with nonstick spray and set aside.
In a mixing bowl, whip the egg whites and cream of tartar on high speed until stiff peaks form set aside.
In a second mixing bowl, combine together the coconut oil, 3 tablespoons of the sugar, and the egg yolks. Add the flour, almond extract, and baking soda and mix just until smooth. Stir in the shredded coconut until the flakes are well distributed throughout the batter.
In a small bowl, combine the remaining coconut sugar and the blackberries. Lightly mash until the berries are only slightly chunky. Gently fold in the blackberries and whipped egg whites. Transfer the finished batter to the prepared cake pan.
Bake for 20 to 25 minutes or until a toothpick inserted comes out clean. Cool completely in the refrigerator before frosting.
For the Blackberry Yogurt Frosting
Gently mix together the yogurt, honey, almond extract, and lemon zest in a medium mixing bowl. In a small bowl, mash the blackberries and add to the yogurt mixture and stir just until combined. Refrigerate for 1 hour.
Gently frost one of the 9 inch cakes with the yogurt frosting and carefully place the second cake on top. Frost the top of the second 9 inch cake. Do not frost the sides. Refrigerate until ready to serve and after serving.