Psychmama: the job you want will probably not be posted for a "psychologist" but if you find a job as a mental health practitioner or counselor or case manager or psychometrist or crisis specialist.....any of the social service categories (or research) where a masters in psychology is the entry level degree AND you can get an hour of supervision by a psychologist (plus other specifics yours state might require), you will be on the path. I usually encourage students to look for government (state, county, or municipal) or educational settings because sometimes these are considered "exempt" settings (in a certain regulatory sense) and you don't have to get special pre-licensure credentials (like a psych assistant certificate). Inpatient and residential setting also often have easier access to qualified supervision for psychologists (eg: licensed psychologist or board certified psychiatrist) than do community based organizations. You just have to network persistently and creatively and not look down on "master's level" clinical positions; that is where the entry level work is and there is so much to learn in this profession that you can easily work in a master's level job and be learning as much as you would in a formal post-doc (and sometime be paid more...)
Be sure to read the details of your state's licensure law about supervision carefully--then look for work that meets those criteria and ask in employment interviews (and contract) for guarantees re supervision. It is your job to know what is required. Employers are not responsible for knowing that, but once informed can be motivated to provide it. It is definitely possible to get an employer to agree to provide what you need.
