The only type of paint that I know of that is even somewhat safe it I believe a Krylon type used in childrens rooms and on baby furniture, it is water based and supposed to be low VOS and low chemical. Even with that type of paint it is not suggested to be in an area it will be chewed on. We tried repainting a cage with it and it will scratch off and does not leave a very stable surface. The only other way I know to paint a cage is to see if you have any company nearby that can do a powder type painting. With the powder paint it is baked into the metal of the cage making it almost impossible to scratch off or ingest (notice I said almost
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I know you said your bird would leave it's new cage but could you possibly try removing the old cage completely from the house, placing it outside or in a garage where it is completely unavailable to your amazon and offering favorite treats (hopefully something you don't often offer), and toys only in the new cage for 1-2 weeks to see if your feathered friend gets used to it. If he does not have access to the old cage and is getting "nice" things in his new cage he will get used to it a lot quicker. Many birds don't like changes but will learn to accept them and go on if presented with the change in a favorable/fun manner