What Shader a means by Airlines is Continental, Delta and United all ship birds in approved carriers. Most bird breeders here in the US that are reputable know how to ship the birds they raise with security and safety in mind. The breeders usually have their shipping details listed on their website.
A good site to check out breeders and what they carry in your state and the rest of the US is
http://www.birdbreeders.com Of my 7 parrots I own, only one was shipped by United from Washington state to me in Texas. That was my female Green Wing macaw and she took the 9 hr flight with one layover in Chicago very well. When I got to the cargo desk to pick her up they already had her sitting there waiting for me. She just looked at me and mumbled a bit. I was expecting her to be a screaming mess of nerves, but that was me worrying if she would be ok once she got down here.
Green Cheek Conures are one of the quietest of the smaller species and work very well in apartments where noise can be a concern. They are very loving and sweet. When they are first weaned and come home to you they tend to be a bit more nippy, but gentle training and lots of interaction bring gs them out of it by the time they reach their first hatch day.