Heat oven to 350°F. Into cookie dough, work flour and coconut extract.
On well-floured work surface, roll out dough into 14-inch disk. Fit into 9-inch glass pie plate. Trim edges, then flute (use trimmings for cookie-making, if desired).
Bake crust in 350°F oven 30 minutes or until golden. Remove pie plate to wire rack; let cool.
In food processor, blend blackberries until pureed. Strain through sieve placed over glass bowl.
In small saucepan, combine 2 tablespoons of the sugar and 2 teaspoons of the cornstarch. Stir in blackberry puree. Over medium heat, bring to a boil, stirring constantly; cook 1 minute or until thickened. Scrape into medium-size bowl; cover with plastic wrap. Repeat steps 4 and 5 with the raspberries and the remaining 2 tablespoons sugar and 2 teaspoons cornstarch.
In small saucepan, sprinkle gelatin over top of milk; let stand 1 minute to soften. Place pan over low heat; heat, stirring constantly, until gelatin is dissolved. Let cool slightly.
In bowl, beat cream on medium-high until stiff peaks form; refrigerate.
In large bowl, beat cream cheese until smooth. On low speed, beat in cream of coconut, the cooled gelatin mixture and the vanilla extract. Then beat on medium-high speed until smooth. Place bowl over ice water bath; let stand, stirring occasionally, until thickened, about 5 minutes.
Fold whipped cream into cream cheese mixture. Spoon 1 cup of mixture into crust, spreading evenly over crust.
. Measure out 1/4 cup blackberry puree and 1/4 cup of raspberry puree; reserve. Drop alternating teaspoons of the remaining berry purees onto filling. Spread remaining filling over top. Drop alternating teaspoons of reserved purees on top. Drag knife through to swirl. Chill 2 hours or overnight until firm.