I feed mine Noble Goat by Purina, a smidgen of oats and sweet feed and minerals. They have all the brush and grass they could possibly want during the day. I also give treats now and then, raisins and vegetables.
I second the suggestion of the Black oil sunflower seeds. My one goat looks 100% better since I have started giving him the sunflower seeds. His coat when I got him was rough, dull, dry and shedding alot. I am not noticing as much shedding and his coat is becoming very soft, even my daughter who is 4 noticed that he was softer.
I feed all the normal stuff like everybody plus they have plenty of free range... But, when I let them out in the yard with us they push each other out of the way and any body else to get at my Black Walnut Trees. I freaked out at first because they were on the bad list, but they have been fine go figure.