Prepare blackberry syrup ahead of time. Place fresh blackberries, sugar, and water in a small sauce pot. Set over medium heat and bring to a boil. Remove from heat. Use a muddler or fork to break up the blackberries. Allow mixture to cool before straining. Keep in an airtight container and store in the fridge for up to 2 weeks.
In a blender (or food processor), pulse together frozen pineapple and pineapple juice until smooth.
Alternate adding one to two tablespoons of pineapple mixture and one teaspoon blackberry syrup inside popsicle mold until full. Cover mold and insert wooden stick into each cavity. Freeze for at least 4 hours until frozen solid.