Preheat oven to 325°. In a large bowl, beat the eggs, sugar and oil. Combine the flour, cinnamon, baking soda, baking powder, allspice and salt; gradually add to egg mixture. Stir in carrots.
Fill 24 greased or paper-lined muffin cups two-thirds full with batter. Bake until a toothpick inserted in the center comes out clean, 20-25 minutes. Cool for 5 minutes before removing from pans to wire racks.
For frosting, in a large bowl, beat cream cheese and butter until fluffy. Gradually beat in confectioners' sugar until smooth. Stir in the coconut, pecans and raisins. Frost cupcakes. Store in the refrigerator.