Courthouses cost too many hammers for what they do early game, and cities as close to your capitol as Rajavihara are going to have barely any distance maintenance so they'll take even longer to pay the
investment back. City governors are also notorious for running Spies basically whenever they have air to breathe, despite the fact that
is usually less valuable than the
a Scientist provides, although ideally you should never let a city governor make a decision without you double-checking it anyway.
Now after you've industrialized and are spreading one or two powerful corporations that drastically increase city maintenance, definitely build Courthouses. Alternatively, if you're expanding through warfare and end up capturing many relatively far-flung cities, build/whip Courthouses in the new cities to help stabilize your economy. Assuming you still need a stable economy, of course.
As for Lib, if no other AI can research it (I'm
assuming the one AI with Education doesn't also have Philosophy) you can delay it to try and get a better, more expensive tech for it. Military Tradition or, better yet, Rifling instead of Nationalism (or Guilds?), for instance. If another AI
can research it my personal advice would be to just grab it, but that's just me. Ideally you'd delay it a few turns if it allows you to grab a better tech, if your only competition is a relatively slow techer and could also go for Economics first or something, but someone else should go into detail about that. There are situations where delaying Lib a few extra turns is a safe enough bet and worth it, but I personally never bother.