Beat the sugar and oil together well. Add the eggs and beat, just until combined. Next, stir in the bananas, coconut, and pineapple. Finally, stir in all of the dry ingredients, combining well.
Grease and flour a 13x18 jellyroll pan. Pour the batter into the pan and bake for 30-35 minutes at 350 degrees. Do not overbake. Cool completely, before frosting with the recipe below or a cream-cheese frosting.
For the frosting: In a heavy-guage saucepan, combine the flour and milk. Heat to boiling, stirring constantly, until the mixture forms a very thick paste. Be careful not to scorch it. Cool completely - ok to put in the refrigerator for this to happen more quickly.
Once the mixture is cool, cream the butter and sugar. After that, add the milk and flour paste a little at a time, beating thoroughly after each addition. Keep beating, until the frosting is creamy/fluffy. Finally, add the vanilla.