Elastic Beanstalk has built in support for RDS. But, I want to use Postgresql with Elastic Beanstalk. Which will be the best approach for doing this?
You can set your custom postgres database running anywhere and make your rails application to use it from your database.yml file settings.
You can get a hosted postgres instance on Heroku Postgres - it gives very nicely formatted configuration details for ActiveRecord. You just have to get them in your database.yml file.