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.
Whisk the rice flour, amaranth flour, tapioca flour, baking powder and salt together in a medium bowl.
In another medium bowl, beat the eggs and sugar with an electric mixer until light and foamy, about 2 minutes. While beating, gradually pour in the butter and then the vanilla.
While mixing slowly, add half the dry ingredients. Then add all the milk and follow with the rest of the dry ingredients. Take care not to overmix the batter. Divide the batter evenly in the prepared tin.
Bake until a tester inserted in the center of the cakes comes out clean, rotating the tin about halfway through, 18 to 20 minutes (10 to 12 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.