How can I set up an Amazon RDS for PostgreSQL database to act as a replica to a non-RDS PostgreSQL database?

Solution 1:

At time of writing no, you can't.

See:

  • https://dba.stackexchange.com/q/61305/7788
  • https://dba.stackexchange.com/q/66372/7788

Please nag them, both on the forums:

  • https://forums.aws.amazon.com/message.jspa?messageID=547192#547192

and via any AWS sales/support contacts you may have.