I don't think there is a way, as sad animals are the result of area overcrowding. With pigs you can capture them and move them, but chickens and butterflies can't be caught or moved. I think I've heard that they will eventually remove themselves from the area, though?
There is a workaround, but it's expensive: potion of Animal Youth will regress an animal to chick, caterpillar or piglet stage, and they can then be picked up and moved. It can be worth it if you really want to take your animals with you when you move house, tho.
I think that once you get high enough AK you should be able to move chickens and butterflies. Once i was in a street where there were about five butterflies on the ground because they were over crowded and i couldn't do anything!!!