In another bowl, whisk together oil, sugar, eggs and vanilla. With a wooden spoon beat in flour mixture until well-combined. Stir in carrots, pecans and coconut until just combined. Fill muffin tins two-thirds full with batter. Bake in middle of oven until a tester comes out clean, about 18 minutes.
Turn cupcakes out onto a rack and cool completely.
Muffins tins may be used immediately, with fresh liners, for remaining batter. Spread icing on cooled cupcakes and decorate with chopped pecans or toasted coconut, if you like. Add vanilla and drained pineapple and beat again. Icing may be made 2 days ahead and refrigerated in an airtight container. Soften at room temperature before spreading.