Buccanary Coins are collectible coins in Owlboy. They were hidden around byBuccanary, and if you collect enough, she will give you Trinkets in exchange at the Legendary Adventure Emporium. Buccanary Coins can be found by flying through Coupon Rings, pulling up items from the ground, destroying some types of obstacles, and finding chests. Collecting a lot of Buccanary Coins earns you the Treasure Seeker achievement, and collecting all of them earns you the Treasure Seeker Grand Master achievement.
Coupon Rings[]

Collecting a Coupon Ring will earn you 3 coins per ring. Most can be collected by simply flying through them, but some need to be flown through in a set, in any order, to collect all of them.
Coin Chests[]

A red chest in the ground (left) and Otus extracting it (right).

A blue chest on top of the ground.
There are several varieties of chests in Owlboy that yield a variety of coins. Chests found in the ground simply need to be pulled up and out. Chests that sit on top of the ground have buttons that need to be pressed and released by Otus or one of his party members. Red chests can be found generally in the overworld, in secret rooms hidden behind walls, or after completing a challenging optional room, and blue chests can sometimes be found after clearing a room of all enemies.