Preheat the oven to 300 degrees F (150 degrees C) using the convection setting. Grease 2 cookie sheets with 1 teaspoon coconut oil each.

Mix coconut flour, cream of tartar, baking soda, and salt together in a small bowl.

Combine mashed bananas, eggs, 1/3 cup coconut oil, and vanilla extract in a separate bowl. Beat with an electric mixer until creamy. Slowly add the flour mixture while continuing to mix.

Drop spoonfuls of cookie dough onto the greased cookie sheets. Flatten cookies using the back of the spoon.

Bake in the preheated oven until no longer wet, about 35 minutes.