Hi there! Congratulations on your 2 sun conures. They're a blast.
I have an 8 year old sun conure who became bitey when he turned about 3 years old (hormonal period). These were not play bites but serious bites, some even drawing blood. It was a bad experience. This phase lasted about 6 months then tapered off over another 12 months or so until it stopped. Now, he just gently nips or nudges with his beak to communicate his disagreement about something (they still need to express themselves).
I'll share with you the worst advice I received (so you won't make the same mistake I did) and the best advice that finally solved the issue.
WORST ADVICE I received:
1) Tap or grab the beak when they bite. As lumbering humans, we might forget how strong we are and what we intended to be a gentle tap or grab can be forceful to our delicate birds. It hurts them and can be viewed by the bird as cruel and aggressive. There are other, more correct ways to react to a bite which I will mention down below.
2) Water bottle spray. I admit I did it once or twice at the prodding of a seasoned bird owner. I didn't know any better back then and I will forever feel guilty about it. Never again. This is a huge breach of trust for your bird. It's rude, incredibly threatening and may cause your bird to develop a phobia of water.
3) The earthquake. Basically I was told to gently shake my bird off my shoulder or arm. This did not help and only caused my bird to distrust the stability of his human perch. It also actually had the opposite effect because he would bite harder to grab hold of me.
4) My old vet actually recommended a wing clip to curb his attitude. This is a controversial subject and people have their reasons for clipping a bird's wings. I won't go into it. One thing I stand by is to never clip a bird's wings to curb his aggression or attitude. He is aggressive because of underlying stressors. Clipping his wings will not eliminate those stressors - it will make it worse.
5) This same vet also recommended an injection that inhibits hormones. Shocking. He said he's done it routinely on some birds (every six months). Some medication can ruin our bird's organs (liver for example). I reserve the use medications for life-threatening conditions, not for a biting bird. He is no longer my vet for this and many other reasons.
BEST ADVICE I received:
1) Understand why your bird is biting. Out of play? Hormones? Perceived threats? Jealousy? By understanding the trigger, we win half the battle by avoiding the trigger (when possible) or teaching the bird that the trigger is not a threat. Teaching a bird that something is not a threat is a whole other topic and one that is still a hit or miss for me. I do want to say that positive interactions with perceived threats over time has changed my bird's perception towards some of them. Positive interactions can mean verbal or tactile praise, treats, showing him that it is safe to interact with the object, etc.
2) When a bird bites, make him understand that he hurt you. How? By mimicking birds in the wild. Do not shout in human-speak. Screech like you're a bird that got hurt. This may not be effective on the first try but keep sticking to it and be consistent. Eventually your bird will understand because he makes the same kind of noises (i.e. I accidentally pinch a not-ready pin feather sometimes). Now when my bird nips harder than he intended, I screech and he scampers to my face to kiss and groom me. Sometimes I keep screeching just to get that special treatment. Hahaha!
3) This is an extension to #2, of making your bird understand that what he did was not socially acceptable. Walk away. Leave the bird, turn your back at him and leave the room. Close the door behind you so he cannot follow - this is important. Shunning is a social response in parrot flocks to punish members who crossed the line. Do not shun him forever though. Go back and give him attention after 15 to 45 mins depending on how serious the offence was. This method was the most effective for me because it not only communicates to the bird that what he did was not acceptable, it also allows you to calm down in another room. Birds sense an upset human very well. IMPT: Make sure that your home is bird-proof so that when you walk away, your bird won't get into anything that would harm him (ex. fans, wires, open doors/windows, open toilets, stoves, other pets, etc.).
Wow, that was a lot of typing! Sorry if I bored you. This topic is close to my heart and I wanted to make sure the advice I received helps someone else who is going through what I went through. Best of luck! Happy parronting!