Combine chocolate, cinnamon, and oil in a medium heatproof bowl and set over a pot of simmering water. Stir until mixture is evenly melted and smooth, about 5 minutes. Set aside to slightly cool and thicken, about 3 minutes.
Meanwhile, line a baking sheet with aluminum foil, parchment paper, or a silicone baking mat and insert sticks lengthwise into the center of each banana. Place toasted coconut in a shallow plate.
When chocolate is ready, tilt the bowl, and, working one at a time, dip the bananas evenly into the chocolate mixture. Tilt and turn to coat the banana evenly. Tilt banana so excess chocolate can drip back into the bowl.
When chocolate is just set, roll banana in the toasted coconut and transfer to the prepared baking sheet. Repeat to coat all the bananas. Place bananas in freezer to set up, at least 20 minutes.