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Preheat the oven to 325F and grease a donut pan very well.
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In a medium bowl, whisk together the coconut flour, sweetener, cocoa powder, baking powder, and salt. Stir in the eggs, melted butter, and vanilla extract, then stir in the cold coffee or water until well combined.
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Divide the batter among the wells of the donut pan. If you have a six-well donut pan, you may need to work in batches.
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Bake 16 to 20 minutes, until the donuts are set and firm to the touch. Remove and let cool in the pan for 10 minutes, then flip out onto a wire rack to cool completely.