I've had three different Blue-crowned conures, and they were all relatively quiet. Of course, there are different perceptions of "quiet". Quiet like able to live in an apartment and quiet like not able to make your ears ring. I would not recommend ANY psittacine birds for apartment living except maybe cockatiels, and some of those can get pretty boisterous.
Edited to add, if you want your ear drums split, get a Sun or Nanday conure!
Actually, female cockatiels are about the quietest parrot I can think of at the moment, and they make great pets. There are several sex-linked mutations in cockatiels (cinnamon, lutino, pearl, yellowface), which would allow for a pairing to produce chicks sexable while still in the nest. So if you ask a breeder (rather than a pet shop) for a female, they might be able to sell you a baby whose gender is known because of this pairing.
But, again, if you want a quiet pet bird, check out mousebirds. They're not parrots, but they can be very entertaining if they're handfed.