Indeed having unencrypted password lying (.pgpass or PGPASSWORD or -W) around is making my auditors unhappy,
With the greatest of respect, perhaps you need to get auditors who understand crypto better.
Having a user that has the minimal permissions to perform the required tasks with a stored password that only the automation user can read is perfectly valid. Encrypting it with a key that must (perforce) be accessible using the same permissions that the user would need in order to to read the unencrypted password file is no more valid (look up "security through obscurity").
Perhaps you could make your auditors happier by restricting that user's permissions to only run a defined function, and make that function do the work that the automation script wants? So even if the attacker can access the password he will still only be able to run that function? (You could even add DOS protection into the function to ensure it's only run so often, if you were worried about that.)