1. In a food processor, combine the dried plums, dates, nut butter, and sesame seeds. Cover and process until the mixture becomes a thick paste. Cover and chill for at least 20 minutes.
2. Place the coconut in a small bowl. Using 2/3 of the date mixture, form 12 balls. Flatten the balls slightly into the shape of a spider body. Using the remaining 1/3 of the date mixture, form 12 smaller balls to make spider heads. Press the spider heads on to the spider bodies. Gently roll spiders in the coconut, pressing to adhere.
3. Using a toothpick, poke 4 small holes on one side of the spider's body and 4 holes on the opposite side. Press one 2-inch length of the licorice into each of the 8 holes. Squeeze the date mixture gently to ensure that the licorice is secured. Repeat with remaining spiders and licorice.
4. Press 2 chocolate pieces into each head to create the eyes. Store in an airtight container in the refrigerator for up to one day.