Mix eggs, maple syrup, milk, and butter together until the ingredients are well-combined. You can do this with a whisk or mixer.
Add the coconut flour and mix it in quickly to avoid any clumping.
Add remaining ingredients and mix until the batter is smooth. Allow the batter to rest for 5 minutes until the coconut flour has fully absorbed all the liquids.
Fill each of the mini donut maker cavities about 1/2 of the way full and cook for 2 minutes once all the cavities are filled. Ignore the indicator light and only cook for 2 minutes once the lid is closed.