On well-floured surface, roll out dough to 14-inch disk. Fit into 9-inch glass pie plate and trim edges.
Bake for 30 minutes or until golden. Let cool.
Blend blackberries until pureed. Strain through sieve over glass bowl.
In small saucepan, combine 2 tbsp of sugar and 2 tsp cornstarch. Stir in blackberry puree and bring to a boil over medium heat. Cook 1 minute or until thickened. Scrape into medium bowl and cover. Repeat with raspberries.
In small saucepan, sprinkle gelatin over top of milk and let stand 1 minute to soften. Place pan over low heat and stir constantly until gelatin is dissolved. Let cool slightly.
In bowl, beat cream on medium-high until stiff peaks form and refrigerate.
In bowl, beat cream cheese until smooth. On low speed, beat in cream of coconut, gelatin mixture and vanilla extract. Beat on medium-high until smooth. Place bowl over ice-water bath and let stand, stirring occasionally until thickened, about 5 minutes.
Fold whipped cream into cream cheese mixture. Spoon 1 c of mixture into crust, spreading evenly over crust.
Measure out 1/4 c blackberry puree and 1/4 c raspberry puree and reserve. Drop alternating tsps of remaining purees onto filling. Spread remaining filling on top. Drop alternating tsps of reserved purees onto filling. Drag knife through filling to swirl.