Additional Conure Species There are many types of conure parrot species. We hope to have this list sorted into small medium and large Conures in the near future. Remember, every conure is a parakeet but not every parakeet is a conure. Argentina Conure Austral Conure Azara’s Conure Aztec Conure Azuero Conure Berlepsch’s Conure Black-capped Conure … Continue reading List of Types of Conure Parrot Species