You can allow remote access for a set IP for postgresql by editing /var/lib/pgsql/data/postgresql.conf file for the following two lines:
Uncomment both lines and then revise the localhost one to listen on another remote IP as well:
#listen_addresses = 'localhost'
#port = 5432
After that, save the file. Then add the following like to the bottom of /var/lib/pgsql/data/pg_hba.conf file:
#listen_addresses = 'localhost,IP#'
After that, restart postgresql in WHM or using "/scripts/restartsrv_postgres" without the quotes in root SSH.
host all all 0.0.0.0 0.0.0.0 md5