I want my dog and cat to not attack my bird if it flies onto the floor when its startled. I have a linnie that chases them away, but the cat always seems to come back in a stalking mode. I watch him very carefully to make sure Pickles doesnt get hurt. I have a medium sized dog that seems to avoid the bird.
I'll be getting a new conure in a few months and I want to get my cat over the curiosity before then. I also want to teach my dog not to bite if the bird bites her first.

Does anyone have experience teaching other animals to be friendly to a parrot?

All animals are wild their instinct need to be respected. In my opinion your bird should NEVER come in contact with your cat no matter how friendly you think your cat is. It is very stressful for birds to have animals "stalking' them. Ideally your birds cage should be in a room where you can shut the door and keep your feathered friends seperated from your furbys unless you're right there. Dogs and cats should be out of the room when you are interacting with your bird. I know you said you watch - an accident with another pet can happen so fast watching isn't going to do anything. As for expereince there is no teaching some dogs won't bother the bird some are deteremined to hunt them down - they have their instincts and you really can't do anything about it. As stated above I don't think you can terach cats ANYTHING including to not attack an animal that is in their nature to hunt. I beg beg beg you to be super careful and not take chances with this new conure.

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Yeah, you can't really train it out of cats, they are built for hunting. Just watch the way your cat plays, almost everything is stalking/fighting.
I would keep my birds locked in the cage if I wasn't in the room with them and there were cats and dogs in there.

My Macaw is larger than my cats and I still don't let her interact with them. those claws and teeth could do a lot of damage very quickly. Cat saliva is also very bad for birds.

There is no way to train your dog not to bite if the bird bites first. It's a natural reaction on the dogs part. I assume 'Training' in this way would have to involve letting your bird bite your dog, which teaches the bird something very bad and risks his life.

Just have to be careful and remember your Birds are prey your Cat & Dog are predators. Good luck with your new Conure!!

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Sarah