Place the cream of coconut, coconut milk, and pineapple chunks in the blender. Puree until the pineapple chunks are mostly blended. Then pour the mixture into popsicle molds about two-thirds full.
Spoon the sliced strawberries out of the thawed syrup and into each popsicle mold, filling it close to the top. Use a popsicle stick to push the strawberries down into the molds to separate them. Then leave a popsicle stick in the center of each pop.
Freeze for at least 3 hours, but up to 5 hours. To un-mold, flip the popsicle mold over and run the tip of each pop under warm tap water. Then gently pull them out.