If you fiddle with it enough, Slony for PostgreSQL can be made to work reliably, but you need to keep an eye on it, and it works by WAL (write-ahead log) shipping and thus can generate quite a lot of traffic. You still need to configure fail-over for the PG clients (i.e. the Discourse node.js code).
However, database replication is NOT a substitute for proper back-ups. Rob seems to suggest that it is, above. It isn’t. DB replication does nothing to protect you from database content corruption, the most frequent cause of which is failed or botched front-end or middleware code updates, and/or being hacked. Either way, the data content rot spreads instantaneously from one copy of your database to the other, and then you have two useless databases…
The correct approach, IMHO, for a site like this, is to move to Amazon AWS (or Microsoft Azure or Google Cloud, but Amazon has the most extensive offerings in every respect), and use AWS RDS (Relational Database Service) in Postgres emulation mode. That gives you a super-reliable, fully-maintained (by Amazon) HA database back-end with no extra effort at all. Use two AWS EC2 servers in a VPC (virtual private cloud) to host the Discourse front-end, with AWS Elastic Load Balancing in front of them, which then both balances load (not really needed) and handles fail-over. Use Amazon Route53 distributed DNS - both secure and fast, and Amazon CloudFlare to provide global CDN (caching) so that the site is fast no matter where you are. Use AWS snapshots stored to AWS S3 storage buckets (which are automatically highly distributed and HA), as well as at least daily dumps of teh database to an S3 bucket. Older back-ups can be shuffled to an AWS Glacier tape store for even cheaper long-term storage if required.
That’s the way to do this properly, and there are even hand-holding guides available for setting up Discourse like this on Amazon AWS. As I said, Microsoft Azure or Google Cloud could also be used, but AWS is probably the path of least resistance.
“But all that will cost too much!” I hear you cry. Well, maybe not as much as you think, and the costs tend to scale with the size of the site and the traffic. But, you know, these things need to be properly financed, on a sustainable basis, if you want to do it properly. A few pounds/euros/dollars a month from a relatively small pool of supporters should be plenty to host it properly (and Discourse even has built-in support for Patreon, so setting up the mechanism for such financial contributions is quite doable).