Preheat oven to 375 degrees. Line 3 standard 12-cup muffin tins with paper liners; set aside. Whisk 2 cups oats, the flour, baking powder, baking soda, salt, bran, and cinnamon in a medium bowl; set aside.
Put butter and sugars into the bowl of an electric mixer fitted with the paddle attachment; mix on medium-high speed until pale and fluffy. Mix in eggs, 1 at a time, and vanilla. Reduce speed to low. Add flour mixture, and mix until just combined. Mix in sour cream. Stir in raisins with a rubber spatula.
Transfer 2 3/4 cups batter to a small bowl, and stir in remaining 1 3/4 cups oats and the coconut; set aside. Spoon 2 1/2 tablespoons plain batter into each prepared muffin cup; top with 1 1/2 tablespoons oat coconut batter. Bake until golden and a cake tester inserted into centers comes out clean, 18 to 20 minutes. Transfer to wire racks; let cool completely.
Cupcakes can be stored in airtight containers at room temperature up to 3 days.