Like laurasea said, I just put both my females in the same cage, I'm sure they have a spat or two probably started by the baby Zod, but for anything minor I just let clark be the alpha female and there has been no blood lost or even a feather. Usually when I see them spat it's more of a "NO! AND CHIRP!!!". and the pecking order got it's name from....well just that; bird interpersonal relationships. (note if I hear a loud chirp I put myself between them, got a few bites but nothing really hard at least to me.)
Also what EllenD said both conures still come to me at ANY time of separation, and make contact calls for me, but not eachother. Basically they both think they are people.
Also what EllenD mentioned....I know this will make peoples upset but let them have a few tussles...let them fight in front of you just to gauge how serious it is...if it's not....then your fine. At most have two food bowls available so they don't fight over food. there will be an alpha and a beta, once tht is resolved there won't be anymore fighting....at least until the smaller one gets bigger.
I give both birds equal time and affection and, usually 90% of the time, they are preening each other. I think the spats come when the new one is more nippy and clark doesn't like. Still working on bite pressure.
I wouldn't worry so much, if anything you MIGHT (AND I AM NO EXPERT HERE) you might be prolonging the feelings by not letting them settle things out themselves.
I agree with this to a point, but there is a huge difference between a "tussle" and an actual fight...And we also need to remember that there reactions are much different out in an open area than they are when they are locked in an enclosed area...Fight or Flight is a very real thing, and if two birds are locked inside of a cage and they have what would typically be a small "tussle" between and alpha and beta or dominant and submissive birds, inside of a small, enclosed area that they cannot get out of, that "tussle" can quickly turn into a very violent fight that can result in cracked/broken beaks, punctured eyeballs, and bite-wounds that bleed a lot...And Green Cheeks are small birds that do actually die after losing only 2 Teaspoons of blood...That's it, that is literally the amount of blood a Green Cheek Conure can lose before dying...And if they lose anywhere near 2 Teaspoons of blood and they live, they will be severely Anemic and their Blood-Pressure is going to tank...Blood-loss is the #1 reason that birds die during surgery; most people think that it's the anesthesia that kills birds during surgery, but that's not the case at all, it's blood-loss. They just don't have much blood in their bodies to begin with, and once they lose around 1 Teaspoon their Blood-Pressure drops so quickly that this is why their hearts stop beating.
So keeping that in-mind, all it takes is a toenail being ripped out, or a bite-wound to a very vascular area of their bodies like their necks, their eyes, a toenail, the upper part of their beak, etc. and that's it. If no one is there to immediately put pressure on the bleeding and slow-it/stop it, they will die quickly...So the bottom-line for me is always "Is the risk worth the benefit?"...
I had a friend who lost their Sun Conure due to a fight that he had with her Jenday Conure. They were both purchased at Petco at the same time as very young, hand-fed baby birds, and they both had their own cages and didn't live or sleep together in the same cage, but they were together whenever she was home and they were out of their cages...They were very bonded to each other and to her, and they did have exactly what Clark describes as "Tussles", just like most birds have from time to time...She had run out to the grocery store to pick-up a bag of dogfood, and the birds were out flying around the house, having a good time, and she lived 5 minutes away from the store, so she figured it would be fine, so she just left them out, told them she would be back in 10 minutes, and she left...She said she was gone for no longer than 20 minutes, and when she came back her Sun Conure was laying dead in the bottom of his own cage in what she called "an ocean of blood"...Now Sun Conures don't have that much blood in their bodies, so she was just so traumatized by what she saw that it looked like "an ocean of blood", but it was probably only around 2 Teaspoons or so of blood...
The only wound on her Sun Conure anywhere was to it's eyeball...The Jenday took the majority of the fight, he was covered with bite wounds all over his body, and he had a small crack to his beak, and a very bad bite to his wing...But the Jenday lived and was fine...The Sun Conure had one, single puncture wound to it's eyeball...Behind the eyeball of pretty-much all animals, including humans, is a large Sinus (big blood-vessel) that provides blood supply to the eye and surrounding tissue...And when the Jenday punctured the Sun's eye, it also punctured the Sinus behind the eyeball, and the Sun Conure literally bled-out through that Sinus behind it's eyeball...Such a freak thing that happened, not even a bad fight...But apparently the Jenday Conure decided to go inside of the Sun Conure's cage, and the Sun became territorial about it's cage, and they got into a fight, and unfortunately the Jenday managed to put it's beak through the Sun's eye, and that was it...
These are the kind of freak accidents that can happen, and these are the things that make me always stop and ask myself "Is this worth the potential risk? Does the overall benefit out-weigh the risk?"...And usually the answer I get is a resounding "NOOOO"...