I can get untreated pallets for nothing from a local transporter. I break them up and use a hole saw to cut 'biscuits' (cookies) out of the timbers. I drill holes in the biscuits and string them on paulie rope for the birds to play with. The remaining 'holey' timber is simply pushed through the cage bars to make a (temporary) extra perch. The birds turn it into matchwood in no time flat!
Native timbers are the best, though. You'd need to check what's safe in your area, but I know that Australian Eucalyptus, casuarina, bottlebrush, paperbark, grevillea and hakea are all fine for birds. Whenever I'm driving through bushland, I'm always on the lookout for fallen branches which can be stripped of their bark and turned into lovely smooth natural perches by my birds.
My dear old galah, Dominic, was famous for eating one entire architrave off the top of our back door! He did it all by himself, inside a month and my poor husband was nearly in despair ('I'm married to a woman who just stands there and smiles while her bird literally eats us out of house and home!') He overdramatises, though. He put up a new architrave and Dommie didn't eat much of that.
If you can get really thick cardboard tubes (like packing cylinders or the bolts that fabric is sold on), you can drill holes through it and stick in stainless steel bolts. Secure them with stainless steel wingnuts and your birds will have a ball unscrewing them! (NB. Tie a bit of chain or leather to each wingnut to prevent them getting lost).
I have almost as much fun making toys for my birds as I do actually playing with them!