Peel the bananas and insert one popsicle stick into the cut end of each banana. Place the bananas on a parchment-lined baking sheet and freeze for at least two hours until firm.
Combine the white chocolate chips and coconut oil in a microwave-safe bowl. Heat in 20-second intervals, stirring between each, until the mixture is fully melted and smooth.
Remove the frozen bananas from the freezer. Dip each banana into the melted white chocolate, turning to coat evenly and letting excess drip back into the bowl.
Immediately press three or four mini chocolate chips into the white coating on each banana to form eyes and a mouth. Return the coated bananas to the baking sheet.
Freeze the pops for another 15 minutes until the coating is set. Serve straight from the freezer.