Agree with the PP. They can be composted, but it might bring in scavenger type predators (possums especially)
I bury the pet birds near the coop and put a brick over it, but we don't have too bad of a pred problem in our yard - probably because of the dogs. I usually let the dogs snif the dead bird, they know the birds are family and they seem to understand death, the dogs have not dug up a chicken either.
Some of the roos that live out at my in-laws in the sticks that predators got, I left them laying out coz I couldn't retreive them due to the fire ants and I think possums took them by the next day.
I usually dump dead preds off the road near the sewage treatment plant (away from houses obviously) and scavengers usually take care of them too.