In my experience petting is not an option and my keets are tame and lovable. I have tried the belly, under the chin, the wings or side and even used my nose to try to rub their bellies. All of this action is met with reactions ranging from flying away to right out beak attacks.
This kind of interaction seems to go against their instincts and hasn't worked for me. I have one that likes to cuddle under my chin and that all I get.
I know some people can scratch and pet their birds. I would love to go to belly scratching school if that was an option