I have a Postgres SQL Server in my Google cloud account (account a). I can access it using the external IP address locally or using the internal IP address from one of my virtual machines.
I have a friend who has another google cloud account (account b). He can't access the account unless I white list his VM's ip address. Is there another way he can access my SQL Server such as adding or changing the IAM permissions?
You can use Cloud SQL IAM database authentication. Note that this feature is on Pre-GA and it is only available for Cloud SQL with PostgreSQL but basically Cloud SQL is integrated with IAM to help you better monitor and manage access for users and service accounts to databases.
Something other thing to take into consideration is that at this time groups are not supported, only direct user and service accounts are (i.e., indirect users via groups is not supported). You will need to give your own user account the "Cloud SQL Instance User" role as well as those user accounts in that group that will use IAM based authentication to the Postgres instances in this project configured to use IAM based authentication. Note that you need at least one individual user account assigned this role in the project - you cannot just have service accounts.
On the other hand, make sure that the Postgres instance you are attempting to add a user to has been set with the flag cloudsql.iam_authentication as per the instructions here.
Next, you should be able to add the user and Service Accounts granted the "Cloud SQL Instance User" role via the 'Add User' interface as described here.
Finally, you'll need to GRANT each user/Service Account appropriate permissions on the schemas it should have access to, pay attention to the fact that the full email address of the user or Service Account is required as outlined here.