Sure, a conservative billionaire could take over the NYT. But who would want it? It loses money and the entire staff will still be a gang of liberal hacks.
If a conservative wants to get into the printed news business he's better off starting fresh. He'd still have to hire a whole new staff of writers but he wouldn't be stuck with increased unemployment taxes, pensions, and healthcare from all the liberal stiffs he'd have to can if he bought the NYT.