Divide cream of coconut into 3 separate bowls for the 3 flavors. Optional: for any of the flavors, if you don't want a strong coconut taste, then add a little milk (under 1/4 cup as it will change the texture)
Add strawberry juice from mashed dethawed frozen strawberries and add to one of the coconut bowls. Hand combine in bowl or use a a blender for find strawberry pieces.
For the chocolate bowl, add cocoa to another coconut bowl. Add until you get the chocolate ice cream color (or use the egg yolk method).
For the white coconut bowl, add chopped dates.
Chill the bowls for half an hour or longer.
Add each individually to the ice cream maker. Start with the white so the color doesn't bleed. Then do the strawberry and chocolate.