This is somewhat tangential to your question, since it concerns a time period after the 50s and 60s, but in places where the KKK were strongest like Alabama there simply weren't any black state police officers during the 1950s and 60s. As far as other local law enforcement officials such as sheriffs, I don't know of any black sheriffs being elected during that time period. At the state level, a black officer was not deputized in Alabama until 1972, as a result of an extensive court battle led in part by the Southern Poverty Law Center in a case called Paradise v. Allen.

However, even after black officers were deputized into the Alabama state police, they still experienced extensive discrimination in both hiring and promotion. By 1979, no black officer had been promoted, which led to another round of legal battles culminating in the 1983 consent decree that required one black officer to be hired or promoted for every white officer. To this day, it is the most extensive affirmative action program ever to pass Supreme Court scrutiny (see U.S v. Paradise, 480 U.S. 149 (1987)). Having won at the supreme court the case was returned to the district court where it was not ultimately settled until 1995.