As long as my birds have their formulated feed available to them, I give them a pumpkin or squash, and replace it when it's gone. They especially like them when they have gone through a few freeze/thaw cycles, and turn into a pumpkin slushee.
They currently have 2 overgrown zucchini in their run. They've worked on them, but not finished them. What they don't eat simply becomes part of their deep litter. If birds have constant access to greens and such veggies, they will eat them in moderation.