To give a full answer, 'all' details are necessary. The vibrations could be caused by one of several single causes, or two or more in combination.
Some few points to check out to start you off:
1. Pressure class of valve equal to static pressure plus 20% for pressure peaks?
2. Ball valve anchored and supported separately? Piping and equipment before and after valve supported and mounted not to transfer weight or not allowed forces to valve?
3. Is the ballvalve constructed for the purpose, and able to handle the actual water speed? (Simple ball-valves might not be constructed for forces enacting when closing above a certain given speed) In most cases at least trunnion mounted, or better double eccentric ball valve.
4. If this is a turbine inlet valve (with or without arm and weigtload to close), are the actuator forces sufficiently strong enough to close properly? (Not 'riding' on the 'almost closed' flow?)
5a. Are the actuator and actuator mounting supported directly on valve?
5b. If the actuator is mounted on the valve with external support in addition (for instance on walls or floor) will external support, plus actuator movement transfer forces, give an influencing skew torque to valve body (in addition to correct torque to spindle)?
6. Are all pipeline components aligned?
7. Any abrupt pipe components after the valve (bends etc)?
8. If this is outlet or bypass valve (also elsewhen): swingings could come from to high throtteling under certain circumstances if the valve is not constructed strong enough for this. The throtteling could give cavitation conditions (vacuum by high speed) and swingings when reentering to 'normal pressure'. (Other type of valve and/or special air inlet necessary)
8. Actuator speed and control OK?
Hope theese hints will help you!