In a small saucepan over medium heat, add blackberries and water. Cook until berries burst. Let cool to room temperature.
When ready, in a popsicle mold, layer yogurt and blackberry puree until all is used up. Cover the popsicle mold with the cover and stick popsicle sticks into the center.
Freeze until firm, about 6-8 hours.
To un-mold, carefully run mold under hot water, careful not to get the actual popsicle wet.