CNAs can do private duty home health care. I see ads for CNAs/HHAs all the time. Usually they will earn more money by working for a private party who can afford to pay them more. But a CNA can not do private duty nursing because a CNA is not a nurse. Only LPNs and RNs can do private duty nursing.
There are agencies for CNA's. I was going to say the same as caliotter....you aren't a nurse, so you can't do PDN. You can, however, do private duty as a CNA. I see agencies and families posting on craigslist all the time.