Hello Alex, and welcome to the Parrot Forums family!
A few questions. Where are you in relation to the cage, on average, when Rio starts to bite? Does it happen more often when you're near to it?
And do you free-feed Rio (food is constantly available in the cage) or do you have pre-determined meal times?
I ask about the feeding times because much of what I'm about to suggest is aided by pre-defined mealtimes. My eclectus parrots, for instance, are not free-fed. They get two large meals per day. (Some do three, in smaller portions. It's fine either way, so long as you are consistent.) Why is there a training advantage to designated mealtimes? Because I get to know when they are at their hungriest and, therefore, at their most treat-motivated. Now, don't confuse this with withholding food for performance. I abhor that practice. The difference is simple, yet vast. They get their meals at the designated mealtimes every time. Regardless of performance. Withholding food is cruel. No, what they are earning in this instance, is the chance to have a little something extra... when they most want it. Strategically-timed training.
So, let's say dinner is at six. (Just an example) You might engage him with a lesson at 5. He'll be at his hungriest, and therefore at his most treat-motivated. You'll be surprised how quickly they pick things up when properly motivated. When he does as you ask, praise him for it. Always use the same words and tone. This consistency is important, as he will begin to associate the words and tone with the treat he so enjoys. (Of course, you will have learned his favorite treats beforehand and made sure they are never in his regular meals. They should be something that he only gets while training.) Association is how birds tend to learn.
And when he doesn't perform as expected, he doesn't get the treat. But be reasonable with your expectations. Baby steps. Don't set him up to fail.
And when dinner time arrives, let him go to his cage to eat. This is important. He should always eat his main meals in the cage. Why? Because it reinforces the feeling that the cage is his home. A place of shelter and the primary place where his hunger is satiated. This is huge when it comes to timeouts. You don't want him ever looking at the cage as a bad place. Do this little bit of preparation, and it will never be a problem.
Now. The biting. First, check out this thread on the causes of biting:
http://www.parrotforums.com/training/57935-brainstorming-biting-parrots.html Very much worth the read, as it goes into many of the causes of biting behavior. And very importantly, it focuses on avoiding the bite
before it occurs.
Second, here are some threads on bite pressure training and dealing with the bite as it's happening:
http://www.parrotforums.com/training/63988-bite-pressure-training.html
http://www.parrotforums.com/questions-answers/58911-bird-bites-always-2.html
Okay. So you have an aggressive biter. You haven't determined the cause of the biting just yet. But you do know that he can't be trusted on your shoulders. Being allowed on the shoulders is a privilege, not a right, and Rio needs to earn that right. From the shoulder, a bird can go after your face. Step one is not to allow him past your elbows until you've worked past this issue.
Now, I know you're thinking easier said than done. And you're right. It's not easy. But it works, so long as you are consistent enough. There are two things you can implement, here. Either temporarily dial back on outside time and work on target training him through the bars of the cage, or introduce him to a more rigorously consistent set of consequences for any given action... as well as equally consistent rewards for desired behaviors. (Consistency is required with both approaches, but consequence comes more into play.)
Okay, in case you're not familiar with target-training, here is a link to the best video I've seen on the topic:
Beginners guide to target training parrots - YouTube
Target-training is important for two reasons. First, it's a bonding tool. This is because a basis for communication is being forged. Once he comes to understand that performing this task will lead to yummy goodness, he'll come to enjoy training time. Both for the treats, and for the stimulation of earning said treats.
And second, it teaches a valuable skill. It gets him accustomed to going where you direct him.
So, if you target-train through the bars of the cage, you'll be protected from his bites while building the bond between you.
You can also, however, target-train outside of the cage. Given how good a flier Rio is, I'd suggest trying to have the target-training progress into flight drills. Having him fly off a to of that excess energy will make him less likely to bite. A tired bird tends to be a more cuddly bird. Whereas an amped up bird will sometimes bite because he's too excited and doesn't know what to do with himself. (Overstimulation is one of the potential causes of biting you'll come across in the Brainstorming thread)
Another thing that might help is carrying either a small, bird-safe piece of wood or hard plastic around with you. (Small enough to carry comfortably in your pocket or even the palm of your hand, and hard enough to withstand a good gnawing.) And then learn the warning signs for when he's about to attack. When he does, interpose the bird-safe item between your flesh and his beak. This will serve the dual purpose of shielding your hand/arm, and also diverting his attention from you as the object of his ire. Most birds will be distracted enough by this that they will momentarily forget their desire to eat you.
Once you become more adept at reading his moods, you'll be able to prevent many bites simply by not putting yourself in the position to be bitten in the first place.
If he clamps down on you, tell him "No," in a firm, yet even, tone of voice. This is to make sure you're not training him to bite you. You see, when you react animatedly to a nip or bite, he has no point of reference for your decidedly human body language. So if you yell, or jump about cursing up a blue streak, it is entirely possible that he might find the display AMUSING. And then he'll of course prove his hypothesis of cause and effect by doing it again. And again. So try your best not to react excitedly. Keep your movements controlled and precise. Keep your voice calm.
But don't just take it. Remove the beak from your skin, say "No," and immediately put him back in his cage on timeout. There is no interaction during timeout. Leave the room if at all possible. Or, at the very least, turn your back. This should go on for 5-10 minutes. Long enough to be a significant consequence, but not so long that he's forgotten that he's on timeout in the first place. When you taker him back out, don't hold onto any of the negative energy from before. Clean slate. If he bites again, wash, rinse and repeat.
Consistency is key. Depending on how stubborn he is, it might take a while. But he'll eventually get it. I rarely have to put my birds on timeout anymore. We understand each other very well.
And yes, the no shoulder part will be tough to enforce. But you just have to out-stubborn him. Tough, but not impossible. And every bite gets him a timeout. A nip that is merely uncomfortable rather than painful might get a warning, "No," first. But a second such nip ends in a timeout as well.
I apologize if this is a bit more rambling than my usual. Long day at work and I'm a bit tired. But if you have any questions, just ask away.
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