The easiest place to charm a Crane is in Minister Cho's Estate, where one can be found just northeast from Minister Cho's Menagerie. You'll have to fight through a few Sickened creatures to get there.
In Pongmei Valley, besides the usual low-level animals, a couple level 15 Elder Cranes or Tigers also spawn near the Yeti in the southeast. By flagging your heroes/henchmen off the radar to the yeti's spawn point, they can be killed/interrupted before they can charm the animals.
Historical note: Originally, the Crane had a red crest and a black neck, very similar to the real-life Red-crowned Crane. Due to Chinese laws against depicting the death of endangered species, however, the Crane's appearance had to be changed in order to keep the game available in China. The coloring of the current model has little resemblance to any real-life crane.