Horizon has shipping containers of various sizes.
http://www.hm-e.net/
Here are the USPS regulations regarding shipping of juvenile and adult birds. Note parts D and E. Also, FEDEX handles the actual shipping between USPS sorting facilities. If they get delayed somewhere (like being bumped off a flight for dry ice) the USPS won't be able to locate them.
9.3.4 Adult Birds
[9-3-13] Disease-free adult birds, weighing no more than 25 pounds, may be mailed domestically. Mailers must comply with all applicable governmental laws and regulations, including the Lacey Act, the Endangered Species Act (ESA), and regulations of the U.S. Department of Agriculture, U.S. Fish and Wildlife Service, and any state, municipal or local ordinances. Mailings must also be compliant with the guidelines provided in USPS Publication 14, Prohibitions and Restrictions on Mailing Animals, Plants, and Related Matter, Chapter 5. In addition, each container or package must be marked as required by U.S. Fish and Wildlife Service under 50 CFR 14.
Adult birds are mailable as follows:
a. The mailer must send adult birds by Priority Mail Express in approved, secure containers.
b. The number of birds per parcel must follow the container manufacturer limits and each bird must weigh more than 6 ounces.
c. A mailing container must be used that is constructed by a USPS-approved manufacturer.
d. Indemnity may be paid only for articles that are lost, damaged, or missing contents, and not for death of the birds in transit if there is no visible damage to the mailing container.
e. Postage refunds may not be available if the Priority Mail Express shipment was delivered or delivery was attempted within three days of the date of mailing as shown in the “Date In” box on Label 11.