Put chia seeds, 1 can coconut milk, and agave nectar in a large mason jar or other closed container and shake well. Chill, shaking periodically, until liquid has mostly been absorbed and mixture has a pudding-like texture.
In a large measuring cup with a spout, whisk lime zest and juice, remaining can coconut milk, sugar, and shredded coconut until sugar is dissolved.
Pour 1 to 2 tablespoons of mixture into 3-oz. popsicle molds, then drop in a couple of crushed raspberries, then add a spoonful of chia pudding. Repeat until molds are full. Insert popsicle sticks in molds and freeze until solid, 4 to 5 hours.