When talking to Marnie, choose the supply option, then buy hay, put it in the henhouse, and the chickens will eat it themselves.

The Story of Starry Dew Valley Niu Niu only eats grass on the grass, which is the kind of grass that your character can shuttle at will. I suggest you fence off a pasture around the cowshed and open the door of the cowshed. They will come out to eat grass by themselves during the day and go back by themselves at night.