Preheat oven to 425 F.
Mix sugar and spices in a small bowl.
In a large bowl, beat eggs. Add pumpkin and mix well. Stir in sugar-spice mixture. Stir the coconut milk well and add to the pumpkin mixture.
Pour into pie crust. Bake for 15 minutes at 425°F, then reduce the heat to 350°F and bake an additional 40-45 minutes. A knife inserted in the middle should come out clean. Cool on a rack and serve.