Preheat oven to 350 degrees.
In your KitchenAid stand mixer fitted with the paddle attachment, beat together the butter and cream cheese on medium high until smooth. Add the sugar and coconut oil and beat again until smooth. Add the eggs, one at a time, beating on low and scraping down the batter bowl as needed.
Add both the coconut and vanilla extracts and the cherries and beat on low until smooth.
Whisk together the flour, baking powder, salt and coconut in a separate bowl. Add the flour mixture to the butter mixture in two rounds, beating on low until no flour streaks are remaining in the cake batter. Scrape down the sides of the stand mixer bowl with a spatula as needed.
Spray a 10-inch bundt pan with coconut oil (or similar high quality) cooking spray. Spread the cake batter evenly in the bundt pan.
Bake cake on the center rack of the oven for 60 minutes, or until toothpick inserted in center of cake comes out clean.
Allow cake to cool in pan for about 10 minutes before inverting onto a cooling rack. While cake is still warm, poke holes in top and on sides with a fork. Using a pastry brush, paint the entire outside of the cake with the unsweetened coconut milk, being sure to reserve one tablespoon of coconut milk for the powdered sugar glaze.
Allow the cake to cool and then make the glaze by whisking together the 1 tablespoon of coconut milk and 1 or 2 tablespoons of the maraschino cherry juice with 1 cup of powdered sugar. Drizzle glaze over the top. Serve cake with whipped cream and whole maraschino cherries.