It is more about the individuals than the species in this case. I have a method that I find to be most effective and fool proof, and the least risky of any that I have used. Because you only have one bird right now, it should be fairly easy.
Choose a place in your house where your sun conure spends very little or no time. Not the bathroom, because you are going to be eating there for a while. This should also NOT be the same room as the cages are kept. Just in case you arent already aware, lets go over some big no-nos.
1)NEVER put the birds in the same cage. I am not saying someday they cant be safe together, but they will need their own cages, and they can turn on each other when you think things are fine.
2) Never give anything of your Sun's to the GCC.
3)Never be in a hurry for them to get along, ever take short cuts.
4)Never allow one bird to sit on the other bird's cage. This does nothing but encourage territorial behavior, and promote the biting off of toes - I am not kidding about this, it is very important!
Ok, I assume they will be able to hear one another during quarantine. If this is not true, then after quarantine place them where they can hear one another for a t least a few days. I also assume they are both tame. If they are not tame, do not introduce them until they are. Once quarantine ends, and they have been able to hear one another, place their cages at opposite ends of a room, preferably not the room you would typically hang out with them in, so that they cannot get jealous of one another getting to spend time playing with you while one sits in the cage watching. Pick one meal a day, some will do this at breakfast, some later in the day, it depends on your feeding schedule, but pick a meal. This requires you to feed meals and not just free feed, but it is healthier anyway. Pick a meal, and feed it out of the cage in a room that does not have the cages in it, and that is not a room your sun is likely to be possessive of. Feed each their meal on opposite ends of the room, and then put them back in their cages. Play time can follow, but only if you have two people to play, again, at least on opposite ends of the room. The next day, repeat, but move the dishes closer. You do this day after day until the dishes are touching one another. Feeding is a flock activity, and I have always had the best results by using this method or variations of it. If something goes wrong, simply move the dishes a little farther apart and start from there. Once they have eaten out of dishes that are touching, transition into together play time after they eat. If you feed three meals a day as meals instead of free feeding, then do this at every meal. At the same time, you can be moving their cages closer together as well.
A note about quarantine: I always suggest blood tests along with quarantine, as even with isolation and the stress of the move some diseases will not show themselves. I use Avian BioTech for my tests, so that I can pay roughly $20 per test instead of ten times that amount from a vet. I suggest asking your vet what blood tests are involved in a "full blood panel" through his or her office, and then ordering those same tests yourself independently from a company such as listed above. You simply look them up online, request the test kits (I use blood cards) which should be free, and follow the directions from there. In my mind no quarantine period is effective without this, especially since very few of us can conduct a "true quarantine" meaning separate ventilation systems, full shower and change of clothes and shoes after every interaction, etc.
