Combine the coconut milk and sugar (or alternative sweetener) in a blender and mix on medium speed for 15-20 seconds. Then divide into three equal parts, around ¾ cup each. Measuring cups work great for this.
Return 1 part of the coconut mixture to the blender along with the strawberries and blend until smooth. If you want a deeper red, add a few drops red food coloring and blend until combined. Pour into a measuring cup and rinse the blender container.
Repeat with the blueberries (and blue food coloring if desired).Pour the red mixture into the popsicle molds, filling each around ⅓ full. Freeze for 30-45 minutes until firm. Place the other two parts in the refrigerator until ready to use.
Pour in the white mixture and freeze for 30-45 minutes until firm, then pour in the blue mixture. Add the popsicle sticks and freeze for 6 hours or until frozen solid then remove from the mold and serve.
Notes
To remove the popsicles from the mold run warm water over the outside of the mold to loosen the popsicles.