I used a hands off approach when training Noah. He came to live with me just three days after losing his mate in a flying accident, and he hadn't been handled since he was little (he turned 2 around the time I adopted him). He was a very angry, frustrated, lonely little guy, and he had terrible social skills. I started by clicker training him, then target training. After he mastered all that, I taught him to step up by targeting him onto a perch I'd hold in my hand.
I did this everyday with him, several times a day. After a couple of weeks he started asking me to pet his head, but I was only allowed to use the hand that was holding the perch he was on (yes, it was as difficult as it sounds). Then he started going on my arm and lap. He didn't like hands, so if I wanted him to go on me, I'd have to ask him to step up on my forearm, then I'd reward him. Again, I was doing all of this at his pace. I made sure not to do anything that would make him uncomfortable, and I made sure to establish from the beginning a strong association between stepping up and reward.
Despite us growing quite close, and him really enjoying playing outside of the cage and training, he would frequently have violent outbursts and would attack me without any provocation. He was hand-raised, yet he was never given the proper training or socialization with humans while growing up. Being hand-raised, he likely didn't have an opportunity to properly learn from his parents. When his former family bought him, he was put in an inadequately sized cage where he would spend much of the day with an older female who would yell at him and hit him. They loved each other, but their relationship was often violent, although neither of them were ever injured as a result.
In these two years of life, he was never taught how to express himself in a healthy, non-violent way. So, when he came to live with me, I had to teach him everything he should've been taught as a child. The only way he knew how to express himself was through violence, and I had to endure vicious biting and sudden, uncontrollable rampages (he'd scream, violently attack any nearby humans, and would completely lose control of himself). The only way I could get him to calm down during one of his rampages was to crinkle plastic, since for some reason, parrotlets go crazy for the sound of crinkling plastic.
Often when he would bite, he wasn't just giving warning bites, or expressing the fact that he was frustrated. When he was really angry, which would happen without any sort of provocation, he would intentionally hurt me, biting me as hard as he could repeatedly, piercing my skin, tearing out bits of flesh, and making me bleed. His behaviour was incredibly violent, and I had to resort to giving timeouts since gentle reminders and attempts to reason with him wouldn't work (I tried for months to do everything except for punishing him with timeouts before finally resorting to this method, as my attempts to negotiate with him only ended with him responding with even more violence). He would even go after my mom (he never went after my dad for some reason), and actually attacked her neck one time, trying his best to take chunks out of her throat. He would even try to take chunks out of my arm, and one time he actually chomped down on my lip and wouldn't let go, dangling from it. I knew none of this was his fault, but after months of this it started getting to me.
After putting him back in his cage after one particularly violent incident, I went to my mom and cried. I absolutely loved the little guy, and I knew he loved me, but I felt he was biting and having outbursts just as often, if not MORE often, as when he first came to live with us. The fact that he had such low self-esteem and was so insecure that he felt the need to hurt me to show everyone that he wasn't to be messed with was really upsetting. My mom told me that I had done more than enough for him and that I shouldn't let such a mean, abusive little bird hurt me anymore. What was happening was basically domestic violence. I'm not making light of domestic violence, either. Had he been a larger species, he would've been far too dangerous to handle.
Despite all this, I persevered and continued to work with him. I knew he was an incredibly smart, loving, sweet little boy who couldn't control his anger. As a child, I had been very insecure, and was quick to anger and lash out as a result. He was just like I had been, and I knew that if I treated him the way I would've wanted to have been treated, he would eventually grow out of it. And he did. One day, after four long months of dealing with the little demon, I realized he hadn't bitten me in almost two weeks.
It's been four years since then, and he's a happy, well adjusted, gentle little boy. We're still quite close, but now he lives with his wife, Rosie, and a flock of budgies. He doesn't need me to preen him anymore, feed him by hand, or let him sleep on my shoulder at night. We don't train together anymore, but he's always excited when I go to visit him and the rest of the flock in the aviary, and enjoys sitting on my arm with his wife. He's very sweet, and I completely trust him near my face and toes. I also don't need to ask him to step up for me. All I need to do is offer him my arm without saying anything, and he's more than happy to hop up on me.
Sorry for the long story, but I just wanted to let you know that even with the angriest, most violent of birds, if you train them well and show them love and patience, they'll eventually come around. You just need to make them feel safe and let them know that they're in control and that you'll never intentionally do anything to harm them or make them feel uncomfortable.