Maybe this is a crazy idea, but why couldn't a wealthy conservative simply purchase the NY Times? They could eliminate the obvious leftist slant in that rag. I would only want the new paper to be "biased" toward the truth, however, and actually live up to the definition of journalism:
The collecting, writing, editing, and presenting of news!
News outlets like newspapers and broadcast network news was crying hunger in the 70s and 80s before cable news and computers burst on the scene. It's most likely that no one wants to buy a paper.
These days you could build a paper cheaper than buying one out.