Is there a parrot called a green cheek conure?

It all depends on if they get along. You might want to introduce them to each other before you throw them in a cage together. They may not like each other, or get along, so this could be disastrous. One of your birds could kill the other. Since sun conures are bigger, it may try to bully the green cheek a bit. Being that birds are so intelligent, they need lots of mental stimulation that another bird can easily give. If you are wanting to spend lots of time with these birds, then you may not want to put them in the same cage, being that they will get attached to each other, and not as much to you. *Always remember to supervise your birds when you put them together for the first few times.* If they seem to be getting along, and you want them to spend more time with each other than yourself, then you should be able to put them in the cage together. Still, I would always watch them for signs of aggression.
It is possible but PLEASE take CAUTION!!! Slowly introduce the two birds first by placing them both on a large table at opposite ends. Do NOT place them right next to each other ... they could attack. Allow them to approach each other at what ever speed they would like. Keep a rolled up newspaper hand just in case they do fight. You do not want to place you hand between two biting birds, especially conures. If they do not fight you can try putting them on a perch together, still leaving space between them. When putting them in a cage together if it is possible get a new cage that way neither one of them has dominance over the cage. You may find that they will become good buddies and they may become somewhat hostile towards you... Just give them attention if you want them to remain friendly.