Possible Clues:

• Bird with large, colourful bill
• Sounds as if a brace of such birds is only able to be one of them
• Bird that's said to play that game?
• More than one are able to hear this bird
• Not hard to handle an exotic bird
• Bird said to play at that game?
• Thus, by the sound of it, a brace can be only one bird
• Large-beaked bird
• Bird with large beak
• A bird, having broken out, is capable of