They will probably eat most vegetables (not hot peppers though), but in my experience they prefer stuff that's easy to chew. They love leaf lettuce since it's easy to chip (especially when I am holding it) to bite sizes. They don't like the stem though. You could try giving them ends of raw green beans, but it might be a little hard for them to eat.
My sister's in-laws have chickens and she said the take all food vegetable leftovers (potatoes, carrots, peel etc.) and boil it until it's soft and mash it together (like mashed potatoes). The chickens love it and they say the egg yolk is huge because of this.