Preheat oven to 350 degrees F. Spread coconut in single layer in shallow baking pan. Toast coconut in oven about 10 minutes or until lightly browned, stirring occasionally. Cool in pan.
Meanwhile, with sharp knife, make lengthwise cut along side of each sorbet and ice cream container. Peel off and discard containers. Slice each pint crosswise into 6 slices.
On each of 6 chilled dessert plates, stack 1 slice raspberry sorbet, then 1 slice pineapple-coconut ice cream and 1 slice mango sorbet. Drizzle stacks with blackberry syrup and sprinkle with toasted coconut and blackberries. Serve immediately.