The only thing I could find was a download for the BlackBerry was a widget that creates an icon on the desktop that takes you to the CNN mobile website.
A Google search did show lots of references to the link posted above, but prefaced with Beta in the URL and those references were dated 2008 and 2009.
There is an app labeled as a
CNN Java Mobile Application, but that is noted as only for certain SonyEricsson, Nokia and Samsung phones.
As far as I could see there is no actual CNN App for BlackBerry. Maybe they gave up?