Wasn't there some "Twitter alternative" launched by someone who used HN? Its entire business model was to bill users. I can't remember the name of it, or the founder, but I think the service failed to gain traction.
edit: The service was/is App.net, and it was founded by Dalton Caldwell. It used to make the rounds on HN all the time.
IMO the best way would be to do microtransactions and go whale hunting. For example, you could charge a quarter for every character past the current word limit and a dollar per character after 200 and kill two birds with one stone.
Instead of charging all users, they could offer premium accounts that allowed longer posts, did not display ads, have private circle-like channels that you could post to for closed conversations, etc. They haven't expanded the feature set to take advantage of these opportunities, though, so senior management seems to lack the imagination to drive it towards profits.
I don't know if Twitter has ever spoken about it but the lack of premium accounts has long puzzled me. Surely there are worthwhile features they could offer without degrading the free tier experience. My circles are perhaps atypical but for those of us who use it as a fairly important professional tool, a $50/year pro account would be a complete no-brainer. Maybe there aren't enough people like this to deal with the complications. It seems unlikely they haven't thought about it. But the lack is still surprising.
Most of the people I talk to on Twitter don't have money to spare. They're the kind of people who have to toss up a fundraiser to make rent because they had a surprise medical bill or car repair.