I don't know. The best idea I can think of today is to get rid of advertising-based business model (possibly through regulation) and have all news sites paywalled - but, and here's the trick - make money spent on news stories tax deductible, or even 100% reimbursable.

This preserves the market dynamics and keeps the government from controlling the press, while still effectively making the press government-funded, as it should be, because access to timely and accurate news is a public good.