Make the cake: Preheat the oven to 350°F. Spray a 9×13-inch metal pan with nonstick cooking spray and lightly dust the inside with flour, tapping off the excess.
In a large bowl, combine the flour, cinnamon, baking soda, salt and nutmeg. In another medium bowl, beat together granulated sugar, oil, coconut, vanilla, eggs, banana and pineapple. Pour the wet ingredients into the dry ingredients and whisk until completely blended. Add the pecans. Pour the batter into the prepared pan. Bake until a toothpick inserted in the center comes out clean or the cake springs back when pressed lightly with a finger, 30 to 35 minutes. Let cool for 30 minutes. Transfer from pan to wire rack and let cool completely. Once completely cooled, level the top using a serrated knife.
Make the icing: Meanwhile, in the bowl of a stand mixer fitted with a paddle attachment or in a large bowl with a hand mixer, beat the butter and salt on high speed for 1 minute. Add cream cheese and beat until smooth and fluffy, about 1 minute. With the mixer on medium speed, beat in the icing sugar in three batches until combined. Stir in vanilla until combined. If the frosting is too stiff, stir in the heavy cream, if necessary.
Spread frosting over cake and garnish with pineapple rings and pecans, if using. Cut into 12 equal pieces and serve.