Preheat the oven to 350 degrees F and position a rack in the middle of the oven. Line one 12-cup standard muffin tin or two 24-cup mini-muffin tins with cupcake liners.
Combine the butter, cocoa, coffee and 1/3 cup water in a microwave-safe bowl. Cover with plastic wrap and microwave on high until the butter melts, about 1 minute. Whisk to combine.
Meanwhile, whisk the sugar, rice flour, amaranth flour, tapioca flour, baking powder, baking soda and salt in a large bowl. Beat the sour cream, vanilla and eggs in a small bowl. Whisk the hot cocoa mixture into the dry ingredients. Stir in the sour cream mixture just to combine (don't overmix).
Divide the batter evenly in the prepared muffin tin, filling each cup about three-quarters full. Bake until a toothpick inserted in the center of the cakes comes out clean, about 30 minutes (18 to 20 minutes for minis).
Cool the cupcakes on a rack in the tin for 10 minutes, and then remove from the tin. Cool on the rack completely. Decorate as desired.