What is the best gr alternative that is cheap and can be put in fast?

I have a fairly large back yard that was full of weeds (thistle). My 2 large dogs have completely killed the gr that was barely there to begin with. I have cleaned the back yard out and now all I have is dirt; which is no good due to my dogs. I need to know a really cheap solution to put in my back yard. I am open to putting in some sort of non plant ground cover or growing some sort of very hearty, fast growing, ground cover that can handle the Colorado climate (dry). My yard is about 1800 square feet. Keep in mind that I have very little money to spend on this.