I think the aviator harness is one of the most well known ones and has been rated highly everywhere I've looked.
I have one for Alfie and was starting to get him used to seeing it and putting his head through a loop, but I wasn't able to continue as he took a disliking too me and I had to take a bit of a step back until he calmed down. I would love to be able to get him to wear a harness, but he hates his back and wings being touched and won't even let me give him head scritches at the moment... so it's going to be a long a patient road before I get anywhere close to trying again with him.
There are lots of videos on youtube of people harness training their parrots though- it's a good way to start doing some research.
It make take time and patience, like anything with a grey. The younger you start the process, the better.