In a single piase motor, direction is controlled by the start winding, you need to reverse the polarity of the start winding to start the motor in the other direction. If your motor has the ends of the start winding brought into the connector block on the motor, first job is to identify them, look for Z1 and Z2, or the winding that goes through the centrifugal switch, once you have identified the ends of the start winding, you need a switching set up which swaps them over. Unfrtunaltely some motors do not bring the connection for one end of the start winding into the terminal block, it is buried in the motor windings as a common connection, usually connected to neutral. This type of motor is difficult to reverse, maybe not even worth the bother! If your motor can be mada to reverse by multiple on off switching, there is a fault somewhere!
Phil,
UK