Setting up a local user account for zabbix in the database meant adding this line to /var/lib/pgsql/data/pg_hba.conf:

local   zabbix      zabbix                            md5

Also this psql command to create the user and database – initially you will probably need to do this as the postgres user.

CREATE USER zabbix WITH PASSWORD 'zzzzzzzzzz';
CREATE DATABASE zabbix OWNER zabbix;

Then, as root or any other user, I can create the tables, etc, as described in the zabbix installation guide:

cd create/schema 
cat postgresql.sql | psql -U zabbix zabbix 
cd ../data 
cat images_postgresql.sql | psql -U zabbix zabbix
cat data.sql | psql -U zabbix zabbix