We have 3 pygmy / dwarf goats, even on rations they go through at least a bale of hay a week, the good green hay at that. We supplement with a mineral block also, they get grain when we can afford it, usually to help fatten for winter. Ours are not nice, they are fixed but they still do boy things and we can't let them out because they eat everything.Basically pain in the butt useless lawn ornaments. They don't hurt chickens though.
Are they wasting a lot of hay? I give mine all they can eat, and a small square bale of hay lasts my five Nigerians two weeks usually. And there is almost nothing for them to browse on at all. They do get some grain every evening, too.