Though there is little agreement on the use of backyard, back yard, and back-yard, the trajectory of the language favors backyard for at least the adjectival senses of the word. Right now, while some publications use backyard all the time, some use backyard as an adjective and back yard as a noun phrase, and others use back-yard as the adjective. There is no consistency within the main varieties of English, and some publications are inconsistent within their own pages. The Washington Post, for example, is all over the place:
From Pritchard’s back yard, the game slowly expanded. [Washington Post]
[They] dropped by back-yard cookouts. [Washington Post]
The recent high-school graduate from Landover was lounging in his backyard last month. [Washington Post]
But others do not resist the compounding impulse. The New York Times, Guardian, the Globe and Mail, and the Sydney Morning Herald, for instance, always use backyard instead of back yard, even as a noun—for example:
He later told medical personnel that he had been conversing with a bear in his backyard and hearing voices. [New York Times]
It’s the backyard for thousands of people living in cramped estates. [Guardian]
But last spring we put sod down in our backyard and that’s when the real frustration began. [Globe and Mail]
Standing next to a backyard swing minutes later, the Prime Minister delivered her own appeal to swinging voters. [Sydney Morning Herald]
Still, if you want to be safe, reserve backyard (or hyphenate it—back-yard) for only the adjectival senses, and use back yard when it is a phrase meaning the back part of the yard.