Get the Plants out of the way!!
Using a relatively inexpensive bunk-bed frame, this garden was designed for a small concrete space with a dog. Maria Finn shares this project in her book, A Little Piece of Earth: How to Grow Your Own Food in Small Spaces. The planters which were painted the same pretty purple as the bed frame are on top, out of the way of dogs, and they also provide for a nice small, space covered garden, seating area.
Vertical gardens are very popular and would also be a good option for getting the plants out of the way. But have you tried string gardens? Steve Asbell of The Rainforest Garden shares a great how-to for making pretty rainforest balls (or you can buy one). Imagine a whole balcony full of luxuriant green beauty that Dogs can't touch.
On the design side, forget putting planting beds against the fence. If you want to keep the greenery, Move. Away. From. The. Fence. In fact, take it one step further, and put a solid walkway along the fence. This will give dogs a place to run, it will keep little paws from getting muddy and by moving the plants away from the fence, you not only will have a better chance of keeping them alive, but when they thrive, they will likely obscure the fence and the dog path. Solid paths also can actually train a dog where to run, so get on the dog's level and watch where he goes naturally and design the garden around that.
Give them what they want!
Sunset magazine is always full of great ideas. If you have the space, why not consider a water feature that can also make for a dog splashing area? Also, they have the most comprehensive list I have seen for what NOT to plant in your garden as they are poisonous to pets.
You are trying to live more sustainably, why shouldn't the dog? These dog houses by Sustainable Pets are not only great modern designs, but each are built custom for your pet, come with a green roof, and are constructed from non toxic and recycled materials.
And if all else fails, I recommend Foo Dogs. Sprout Home has a couple great ones, and Amazon has a huge selection too. They are also known as the 'happiness dogs' who bring tranquility and serenity to the garden.