Divide the pudding into 2 small bowls while it's still warm. Add the chocolate to one bowl and stir until well combined. Refrigerate both bowls of pudding, covered with plastic wrap, until chilled, about 30 minutes.
Spoon 1/4 cup of the chocolate pudding into each of 4 ice-pop molds or four 4-ounce paper cups, and freeze for 10 minutes. Remove from freezer and top each with 1/4 cup of the vanilla pudding. Insert wooden sticks and freeze for 3 hours.