I know you can mail bees. When brother and sister-in-law kept bees at their home outside of Boston I recall a loudly buzzing package arriving via USPS. Sure enough, the package contained a new contingent of very healthy bees eager to get out of the box.
Apparently you can ship canaries too, although you can’t ship kittens, or spiders except for scorpions. You can ship day old chickens.
Alas, although you can ship canaries, nothing guarantees that they will arrive in good health. The woman who ordered the canaries, eight of them, was handed a smashed ox with six very dead, mangled canaries inside. No word on the other two.