Preheat oven to 350 degrees F. Lightly grease a 13 by 9 by 2-inch baking pan.
For the cake: In the bowl of an electric mixer, combine cake mix, egg, and butter and mix well. Pat into bottom of prepared pan and set aside.
For filling: Still using an electric mixer, beat the cream cheese until smooth. Beat in the eggs and vanilla. Dump in confectioners' sugar and beat well. Reduce the speed and slowly pour in butter. Mix well. Fold in coconut and pineapple.
Pour filling onto cake mixture and spread evenly. Bake for 40 to 50 minutes.
Don't be afraid to make a judgement call on the cooking time, because oven temperatures can vary. You want the center to be a little gooey, so don't bake it past that point.
Remove from oven and allow to cool completely. Cut into squares.