Preheat oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Beat eggs, maple syrup, and erythritol in a bowl until creamy, about 2 minutes. Add coconut milk, vanilla, and salt; mix well. Mix in shredded coconut until a dense, sticky batter forms.
Take 1 tablespoon of batter and roll into a sphere. Place on the baking sheet. Repeat with remaining batter.
Bake in the preheated oven until set, about 10 minutes. Flip macaroons and bake until lightly golden, about 5 minutes more. Cool on the baking sheet for 1 minute before removing to a wire rack to cool completely.