It all depends on the purpose of your replication. Is it to provide a local data source and avoid network latencies ?
Assuming that your goal is to have cross-region replication, you have a couple of options.
Custom EC2 Instances
You can create your own EC2 instances and install PostgreSQL so you can customize replication behavior.
I've documented configuring master-slave replication with PostgreSQL on my blog: http://thedulinreport.com/2015/01/31/configuring-master-slave-replication-with-postgresql/
Of course, you lose some of the benefits of AWS RDS, namely automated multi-AZ redundancy, etc., and now all of a sudden you have to be responsible for maintaining your configuration. This is far from perfect.
Two-Phase Commit
Alternate option is to build replication into your application. One approach is to use a database driver that can do this, or to do your own two-phase commit. If you are using Java, some ideas are described here: JDBC - Connect Multiple Databases
Use SQS to uncouple database writes
Ok, so this one is the one I would personally prefer. For all of your database writes you should use SQS and have background writer processes that take messages off the queue.
You will need to have a writer in Asia and a writer in the US regions. To publish on SQS across regions you can utilize SNS configuration that publishes messages onto multiple queues: http://docs.aws.amazon.com/sns/latest/dg/SendMessageToSQS.html
Of course, unlike a two phase commit, this approach is subject to bugs and it is possible for your US database to get out of sync. You will need to implement a reconciliation process -- a simple one can be a pg_dump from Asian and pg_restore into US on a weekly basis to re-sync it, for instance. Another approach can do something like a Cassandra read-repair: every 10 reads out of your US database, spin up a background process to run the same query against Asian database and if they return different results you can kick off a process to replay some messages.
This approach is common, actually, and I've seen it used on Wall St.
So, pick your battle: either you create your own EC2 instances and take ownership of configuration and devops (yuck), implement a two-phase commit that guarantees consistency, or relax consistency requirements and use SQS and asynchronous writers.