Halve and pit the peaches. Cut the peach halves into 1/4-inch dice until you have 1 cup. Place the diced peaches in a bowl; set aside.
Cut the remaining peaches into rough 1-inch chunks and place in the blender. Add the remaining ingredients and blend until smooth, scrape down the sides of the blender as needed. Pour the mixture into the bowl with the diced peaches and mix to combine.
Divide the mixture evenly into the popsicle molds, or disposable small plastic cups. Insert the sticks and freeze until solid, at least 5 to 6 hours.