Open the room temperature coconut milk cans. If the fat has separated from the liquid, pour in a sauce pan, heat and stir to create a creamy texture. Let the mixture cool while you prepare the fruits.
Measure out the fruits, set in little bowls and squish with a fork.
Make the White Popsicle Base
Put all ingredients in a blender, and process until creamy. You can taste and if it needs to be sweeter, add a tablespoon of maple syrup if you'd like.
Make the Rainbow Fruit Purees
Add 2 tablespoons of the white popsicle base to each fruit/veggie bowl. Stir with a fork until the mixture is fairly combined. You can add a teaspoon more of the white popsicle base any mixture seems too dry.
Make the Popsicles
Pour the mixture into each popsicle well, filling only 1/3 of the way.
Spoon 2 tablespoons of each color into two wells.
Fill each well to the top with the white popsicle base.
If the rainbow puree appears to be a solid wall between the two white layers, take a fork and push it into the rainbow and tug up and down. You want the rainbow to reach into the white base layers above and below.
Freeze the popsicle mold for at least 6 hours. The longer, the easier the popsicle will stay solid when you remove them from the mold.
Remove Popsicles from Mold
Line a cookie tray with parchment paper and set it in the freezer.
Dip the mold base into hot water either tipping under a faucet or dipping into a large bowl. It's a process. You'll have to dip and tug several times.
As soon as you release each popsicle, lay it on the tray in the freezer.
Store the popsicles for 2 months in a sealed container in the freezer.