No Country was co-produced back in 2006 in a 50/50 partnership between Miramax Films and Paramount. But the real driving force behind the movie's production was a guy with a vision named Scott Rudin (the guy was named Scott, not the vision).
Rudin bought the rights to the Cormac McCarthy novel shortly after the thing came out and then brought it to the Coen brothers to see if they'd direct. The Coens were working on another project at the time, but they saw the potential in Rudin's idea and got to work on adapting McCarthy's book for a screenplay in August of 2005. Good move, guys!