Rachael, my mother in law has a townhome with a small patio on the south side of her house. She has an association there with issues about what she can do with 'her' patio. I sent her some plans from a wordworking magazine for raised containers made out of redwood. These, once built would also confine her small dog to that area. I suggested the green outdoor carpeting. Don't know if she got approval yet but would something like that work for you? You could add a gate of sorts to the 'wall' to get access to the rest of the yard.

The good news is that in our backyard we have actual fencing so it keeps those I want in and those I don't want (hopefully squirrels will get the idea too) out.
I'm not sure if that'd work for us, but I do like the idea of raised beds. I'm just not sure what to do with the rest of the space...