Activate yeast by adding sugar and yeast to warm water. It should double in size.
Heat the milk to be warm. Add the coconut oil and butter to milk, stir to melt.
Beat eggs on medium speed for 4 minutes. Turn off.
Turn mixer on low and add the yeast mixture and milk mixture. Mix for 2 minutes.
Add salt, sugar, xanthan gum, and gluten free all purpose flour. Mix for 2 minutes.
Place ½ cup cup of dough on plastic wrap. Add another sheet of plastic wrap on the top half and gently press down to flatten the ball of dough.
Cut donuts with a donut cutter, remove plastic wrap, and place them on a baking sheet lined with parchment paper. Cover and let rise for 20 minutes.
Heat oil to 275-300ºF and use a candy thermometer to monitor the temperature. Place donut in the hot oil and fry for about 1- 1 ½ minutes on each side. Until it is golden brown. Carefully transfer to a cooling rack and allow to cool for 20 minutes before frosting.