I live in an apartment and own a sun conure which are normally NOT good apartment birds because of their high pitch. I'm in a unique situation so it works for me, but may very well not work for a lot of people- so I wouldn't off-hand recommend a sun.
I live in subsidized federal public housing (not a private landlord) which offers a lot more 'protection' and also Maine law makes it VERY difficult to evict someone for noise complaints (unless they are in the middle of the night).
I am home 95% of the time and when I am home, Skittles is out of his cage and I strongly believe that is why he is so quiet. He can go hours without screaming and when he does, redirection works for the most part. So like I said, my situation is VERY unique.
I don't know much about other conures, but I think green-cheeks might be a good start as far as conures go. Another bird that is perfect for apartment living is cockatiels, budgies as well. But I wouldn't recommend a sun (or any other aratinga conure cause they all have high pitches).