Depending on where you are, this info may not be very useful.
Some places only require a resident to have a medical license to moonlight, some other places require the moonlighter to be a 4th year or board eligible. I would start with calling all the area hospitals, public or private, especially county facilities. For those, you will need to apply for priviledges. Then, I know the disability office is always seeking psychiatrists to do evaluations. I suppose if you search in Google for medical evaluation, disability...etc, this will probably turn up for the area you are in. Disability office outsource this work, so there are companies that hire physicians to evaluate patients, then dictate reports...etc. I think most companies will want you to work a full day on weekends, and they line up patient after patient, you get paid for each patient you see and dictate. I think they end up being abot $60 an hour here in California.
Also, go to the local job fair for psychiatrists, someone is always looking for moonlighters.