In a blender, puree blueberries or blackberries. Strain the mixture through a fine-mesh sieve into a bowl and discard the seeds. Repeat the process using strawberries or raspberries.
Rinse out your blender then blend coconut milk, yogurt, honey, and vanilla.
Blend until smooth and creamy.
Transfer the mixture to a bowl.
Now spoon a couple of tablespoons of both berry purees into your ice pop sleeves.
Using a funnel fill the sleeves with the blended coconut mixture, leaving about a 2-inch space at the top. Top with some more fruit puree, making sure you leave about 1/2 inch unfilled at the top to be able to seal the sleeves. Keep in mind they will likely expand a bit once frozen, so don't overfill.
Seal each sleeve and place them onto a baking sheet in a single layer.
Freeze for at least 4 hours.
Serve and enjoy!