Hmm... That's a good question. If it's safe for them, they generally like it!
Your best chance would be to use plants that you don't mind getting destroyed or putting potted plants in that you can switch out to recover as they get too ratty looking.
Grasses! I use muhly grass because it doesn't have a "bias" so it's less likely to get stuck if they happen to swallow a bit of leaf. My birds (Japanese quail) also use the grass to line their hides and nests.
I've had mine planted for 4-5 years and they just keep growing! I do cut the seed heads off each year because they can be spikey.