So first of all, you need to figure out what your bird's very special "Training Treat" is going to be. This is going to be a food/treat that he loves more than any other treat, and most-importantly is that it's a treat that he ONLY GETS WHEN BEING REWARDED FOR GOOD BEHAVIOR AND THAT'S IT!!! This is extremely important if you want him to actually want to display good behaviors that you want him to do, because he's going to be "working" for that special Training-Treat. That's how smart they are, he will quickly realize that he'll get one of these treats if he does what you want him to do, and that's exactly why Positive-Reinforcement works so well with parrots, because of their high level of intelligence. It's like rewarding a human kid, or even a human adult, by giving them something when they bring home a good report card, such as a toy or video game they've been wanting. That's the best way to get your child to study and do their homework, tell them that if their report card is all A's, then the day they bring it home you'll take them out and buy them the new video game they wanted. And if they can get all A's or an overall GPA over 3.5 or something similar for the entire school year, the day they come home with their last report card for the year you'll take them and buy them something huge that they've been wanting forever, like the puppy they've been wanting for years and years, or the new mountain bike or playstation 4, etc. It's no different for parrots displaying the behaviors that you want them to display, or stop doing the behaviors that you don't want them to display. The only difference between humans and birds is that birds think that the best thing in the world is food, that's what motivates them...And they are a lot cheaper, lol...
So if you already know what his favorite treat in the world is, then that's what you need to make his Training-Treat, and he can no longer get that specific treat at any other time other than when he's being rewarded for behaving well. For example, if your significant other gives you a hug when he's on your shoulder, and he doesn't react at all to him and doesn't bite him or be aggressive with him in any other way, then you give him a Training-Treat. Very important is that whatever you choose as his Training-Treat is small and something that he can eat pretty quickly. You don't want to choose something that he has to hold in his foot and sit and work at eating over the span of minutes, because this is the same treat that you're going to use to work with him on stepping-up with your significant other, and any other things you want to train him to do, like "Recall-Training", which means training him to come to you whenever you call for him. So whatever the Training-Treat is needs to be something you can give him and have him eat quickly so he can move on to the next thing. Good Training-Treats for Green Cheek Conures include Sunflower Seeds that are already unshelled (or Sunflower Kernels), which you can buy at any grocery store or Walmart in bags, because you don't want him to have to sit and take the shell off, you just want him to eat it and move on. I used Sunflower Seed Kernels when I trained my Green Cheek, and they worked great...However, if your bird already eats a seed-mix as his regular diet that contains Sunflower Seeds in it, then you can't choose them to be his Training-Treat (he absolutely shouldn't be eating a seed-mix that contains any Sunflower Seeds, any Nuts (especially Peanuts), or any Dried Corn Kernels or Dried Cracked Corn, as they are absolutely loaded with fat and the #1 reason that they develop Fatty-Liver Disease and die young; there are plenty of high-quality, healthy, low-fat seed-mixes that don't contain any of these things and that are actually high in Protein, Vitamins, Minerals, Amino Acids, etc., and varied so that they don't get bored with their food, such as Tropimix, Higgins California Blend, Zupreem Smart Selects, etc.)...Other great Training-Treats are little pieces/slivers of healthier Nuts that he likes (NO PEANUTS EVER), such as little bits of UNSALTED Almonds, Filberts, Brazil Nuts, Walnuts, etc. Little bits of unsalted Almonds work great. Or, if he really likes a particular fruit, then the dried version of that fruit cut into tiny little bits work well, such as little bits of Banana Chips, Dried Mango, Dried Pineapple, Dried Papaya, Dried Coconut, or any of the fruit "chips", like little bits of Apple Chips/Crisps, as long as they don't have any added sugar or salt on them...
The other really healthy treat for your bird are the cans of "puffs" that are made for human infants/toddlers as snacks. They are all whole-wheat/whole-grain, and none of them contain any added sugar or salt at all, they are simply whole-wheat flour and fresh fruit/water. That's it. I buy multiple cans of these and all of my birds just love them. I buy the Walmart generic brand, and a can of them only costs like $1.50, and they have multiple flavors for you to try to see what he likes best, such as Apple, Apple-Strawberry, Blueberry, Strawberry Banana, Banana, Sweet Potato, etc. My guys love them all. If you were to use one of these as your bird's Training-Treat, you'd need to cut one puff into little bits that he can eat quickly. I'd check them out anyway because they really are a very healthy snack that they love, and what I do is give them one or two of these to munch on whenever I'm eating a snack that I don't want them to have, or that they really shouldn't have, like chips, cookies, etc.
Whatever you choose as his Training-Treat needs to be always ready to give him, so if it's something like unsalted, raw Almonds or anything else that need to be cut-up into little bits, make sure you have plenty of them already cut-up and ready to go...And it's best that you have some in your pocket whenever you're at home, so you're prepared to reward his good behaviors and reinforce them so that he keeps doing them...
*****Now, onto biting....The absolute best way to stop your bird from biting anyone at all is by using something called "The Shunning Method"...There are many, many posts on this forum that explain The Shunning Method in-detail, but I'll go over it briefly here...
The Shunning Method works so well to stop parrots from biting because it immediately takes away what most tame, bonded parrots love most, and that's your attention and acknowledgement. I've seen this method stop a Green Cheek from biting completely within 2 days of using it...However, the key to The Shunning Method working is that every single person who lives in your house must do it and participate in it every single time the bird bites anyone if they are present in the room when he does it. Now I'll be honest with you, the first day of using The Shunning Method is going to be a long day, because you have to do it every single time he bites anyone, and it usually takes them between 5-10 times of doing it for them to realize "Oh, so when I bite anyone this is going to happen to me"...So that means that typically you end-up doing it 5-10 times right in a row, once right after the other after the next, until it clicks. For this reason it's best to start using The Shunning Method on a day where everyone who lives in your house is at home, like a Saturday, and then continue using it on Sunday and from then on...Usually after the first day people find the biting has subsided by about 50%, and as long as you keep doing it every single time he bites anyone from that point forward, it won't be very long at all that the bites stop. You will occasionally have to remind him, but typically what happens is that once the bird stops being aggressive towards certain people, they actually will start opening-up and accepting the person as a Flock-mate. They may never give their complete trust to those people like he will with you or 'his person", but usually will ultimately accept them as a fellow Flock-mate...
I'll write-up a short description of how to use The Shunning Method below, and you can choose to try it or not, but at least you'll have it in your arsenal as something to try if his biting of people in your house continues or gets worse. It's not unusual for parrots to cause stress in people's relationships with their significant other or their spouse, either because the parrot is aggressive with and constantly biting one of them and trying to protect the other who is their person, or even worse is when someone brings home a parrot because they want a bird that they can bond very closely with and have be their best friend who they will care for solely on their own, while the other spouse wants nothing at all to do with the bird, and once the bird is home it ends-up choosing the spouse that wants nothing at all to do with them as "their person", while the spouse who wanted the bird in the first place and who does everything for the bird like feeding them, cleaning their cages, giving them treats, etc.is the spouse who the bird wants nothing at all to do with and may even become aggressive with...This situation has actually broken-up marriages, as they are like human children, especially if we're talking about one of the large Cockatoos, Macaws, African Greys, etc. So hopefully using The Shunning Method will help you significant other to at the very least be able to be with you when the bird is out of their cage without the bird attacking him or being aggressive with him...And maybe he may even start to accept him as a Flock-mate in the future...