We have Ziggi an adopted black cap. Ziggi is a very aggressive bird. He was formerly hit by a previous owner and before that picked on by bigger birds. That being said... he is a doll to Leroy our baby Green Cheek. Leroy is the complete opposite of Ziggi, shy, sweet and quiet (he is the one in my signature), Ziggi is loud, aggressive and outgoing. They are the best of friends and pretty much inseperable. I frequently have to chase them out of each other's cages. They do not agree with my each to his own rule!
I think it really depends on the type of conure, green cheeks and black caps are pretty close in size, whereas (correct me if I'm wrong) a blue crowned is quite a bit larger?
All in all my two get along great, their personalities compliment each other and balance each other out alot.
Leroy also gets on well with Snowflake our lovie girl wheras Ziggi hates all other birds equally! He has even attacked our amazon who I swear just laughs at him!