For the peach layer: Add the peaches, yogurt, extract, and sugar (or sweetener of choice) to a blender or food processor. Blend until smooth. Taste for sweetness and adjust as needed. Set aside.
For the cream layer: In a small bowl, stir together the 1 cup yogurt, coconut milk, vanilla, and sugar (or sweetener of choice) until smooth and well combined. The mixture should be just thinned out enough to pour into the popsicle molds. If too thick, add more coconut milk as needed until pourable. Taste for sweetness and adjust as needed.
Pour cream and peach mixture into the molds alternately, beginning with cream, followed by peach, then a little more cream. Freeze for 30 minutes. Insert popsicle sticks into the popsicles and return the mold to the freezer until firm, at least 2 hours. Enjoy.