To make the papaya cream: In a blender, blend well the papaya with the ice cream until obtaining a creamy mixture. Reserve.
Pour 1 Tbsp cassis cream liqueur or berry coulis into each tall chilled dessert cup, swirl, and top with the papaya cream (or simply serve the plain papaya cream with berries on top). Decorate and serve immediately.
To make the berry coulis: Place the berries, sugar or sugar substitute, and water into a saucepan. Bring to a boil, then simmer for 5 - 10 minutes or until the fruits are soft. Stir in the lemon juice, remove from heat, and cool slightly.
Purée in a blender or food processor; then, strain through a sieve, rubbing it through with the back of a ladle or spoon. Refrigerate.