In a good blender or food processor, combine the avocados, coconut milk, sweetener, and vanilla extract. Blend until smooth. Remove about two thirds of the mixture to a bowl.
Add the berries to the remaining mixture in blender and blend until smooth. If it’s too thick to blend, add another tablespoon or two of coconut milk.
Drop small spoonfuls of each mix in an alternating pattern into 3 ounce popsicles molds. You will get between 8 and 10 popsicles. Tap the popsicle molds firmly on the counter to release as many air bubbles as possible.
Press wooden popsicle sticks about 2/3 of the way into each popsicle. Freeze overnight.
To unmold the popsicles, simply run hot water over the outside of the molds and tug gently on the stick until they release.