Native to the jungles of the Near East, coeurls were only recently introduced to Eorzea, brought over from faraway lands such as Thavnair by Ul'dahn nobles who thought to breed them as pets. Now, but a handful of skilled tamers living in recluse on the Pearl are said to be able to train them.
"Hey, good lookin'! Catch my coeurl yet?" - Swygrael
— In-game description