Special equipment: six 3- to 4-ounce ice-pop molds with wooden or plastic ice-pop sticks (without guards)
Puree the watermelon with 1/4 cup of the sugar in a blender. Pour into a medium bowl and freeze, stirring every 30 minutes, until the puree resembles a slushy mixture, about 2 hours.
Fold the chocolate chips into the watermelon slush and pour into six 3- to 4-ounce ice-pop molds, filling them about three-quarters full. Insert wooden or plastic (without guards) ice-pop sticks. Freeze until the mixture is just slightly set, about 30 minutes.
Meanwhile, mix the coconut milk and 2 tablespoons of sugar in a small bowl and refrigerate.
After 30 minutes, pour the coconut milk mixture on top of the watermelon mixture, leaving a 1/4-inch headspace at the top. Freeze until the mixture is just slightly set, about 30 minutes.
Right before the coconut milk mixture is just set, puree the avocado, lime juice, 1/4 cup of water and the remaining 2 tablespoons sugar in a blender until smooth and creamy. Top the coconut layer with the avocado mixture and freeze until solid, about 4 hours.
Let sit at room temperature for about 5 minutes before unmolding.
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