Have both parties (client & CNA) sign contracts stating they will not work together independent of the agency for a set period of time following their termination of business with the agency without paying a financial penalty.
Travel nurse companies do this all the time. Most travel contracts state that a nurse cannot go to work for a hospital that they worked for with the travel company for at least 6 months after their travel assignment ended. If they do, the hospital has to pay a financial penalty to "buy out" the nurse's contract.