Heat oven to 450°F. Bake pie crust as directed on box for One-Crust Baked Shell using 9-inch glass pie plate. Reduce oven temperature to 350°F. Cool pie crust completely, about 30 minutes.
Meanwhile, spread coconut in ungreased shallow pan. Bake uncovered at 350°F 5 to 7 minutes, stirring occasionally, until golden brown.
In large bowl with electric mixer, beat cream cheese and sour cream on medium speed until smooth and fluffy. Gradually add milk, 1/2 cup at a time, beating until smooth. Add pudding mixes; beat until well blended.
Spread 1/3 of the pudding mixture in cooled pie crust. Top with half of the sliced bananas. Spread another 1/3 of the pudding mixture over the bananas, covering completely. Sprinkle with 1/3 of the toasted coconut. Top with remaining bananas. Spread remaining pudding mixture over bananas. Sprinkle with another 1/3 of the toasted coconut.
In food processor, place mango. Cover; process, using quick on-and-off motions, until pureed. In small bowl, fold mango into whipped topping. Spread topping over top of pie. Sprinkle with remaining toasted coconut. Refrigerate at least 2 hours to chill. Cover and refrigerate any remaining pie.