A training partner has a lab who makes a lot of noise. He whines and usually barks as he is released. It is a very hard habit to break. With some dogs, it is a trait which will not go away with more birds.
Try having someone stand behind you with a horse whip when you have someone throwing you a bird. As the bird is thrown, at the moment he makes noise have your whip man wack him real hard on the backside. You calmly and quitely ignore the whip man and tell him in a even toned voice quiet or no noise. Repeat it a few times then do something else.
Depending on the dog, it may be a good idea to try doing the same drill but, when he makes noise, take him and put him away. Don't let him have the bird. Let him sit for a few minutes then repeat, bird, whip, no noise back in kennel. When he is quiet, let him have the bird.