You should try a pumeria,hibiscus,jasmine sabac,and majesty palms that should give you what your looking for and very easy maintnance just occational pruning.

One of my balcony neighbors had (and I believe still has because I suddenly started seeing the droppings again) a pretty kitty (now cat) who used to lounge under my lilac:

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My sister has a puffy blue-point Himalayan cat who would lounge in her miscanthus grass planted in a half-barrel container when she lived in an apartment. Her cat also liked batting the grass then and still likes this type of grass, which my sister now has planted in the ground at the house she moved into about 6 years ago. Her cat, on her rare forays outside, will go right for it and lie under it.

I think if you get a big enough container (20" or bigger diameter), you could plant something with a wide canopy that the pet can snooze under including something as simple as a ficus (any type, assuming you keep it out there year round). However you may want to make sure that the animal doesn't decide to make your pot their potty as that may cause damage to the plant. You could grow wheat or oat grass for the cats and some kale, parsley, and dill for the rabbit to munch on.

The plants that rixblonde mentions may work, although the plumie may not be able to take constant animal knocking if it isn't secured and there is a potential for branch breaks (and irritating sap oozing). Of course that would equal cuttings too! LOL

Hi lydia, I've recently fallen in love with balcony container gardening and have enjoyed having strawberries and wild strawberries. Tho good luck getting your rabbits not to eat them. >_