Servo motor too noisy
Servo motors use current to force coils to create rotor torque from Magneto-motive force MMF.  They are "often"  called voice coils for the reason that the electro-mechanical motion sounds like a speaker. (unintentionally)

Generally, many devices have software options to reduce acceleration to reduce the frequency range of acoustic emissions.  This is a common feature on hard disk drives (HDDs).

Possible noise emitters:  Motor coil,magnet,gears,piano wire, motor mounts, lack of vibration isolators
 - There are micro harmonic motions and fundamental low frequency motion.
 - The harmonic motions give greater torque by the  gear ratio
 - The high current torque creates a vibration stress and strain with insufficient stiffness
Micromotion

First you must define a system with detailed specs on form , fit and function including environmental noise emissions with other methods to attenuate noise.

Beyond this there is no catalog of noise-free servos, only open ended system design requirements that demand custom R&amp;D solutions. 

Generalized Solution


Test the servo for acoustic emissions.   
Measure the level and determine the amount of suppression required to make it acceptable.  (design goal)
Test other performance parameters for time or frequency and highlight requirements


Identify what causes Piano wire to make acoustic vibrations from both natural resonance and exciter spectrum.
figure out how to attenuate exciter spectrum while minimizing loss of performance.
for example 
measure spectrum of noise and isolate root cause
determine if attenuation is possible by filtering servo current or slew rate or limit.
determine if structure is amplifying Q of the acoustic noise that can be improved by stronger motor or structural support or member (piano wire has very high Q)



caveat

this is just off the cuff method of resolving acoustic servo noise with no problem data, at the time of this writing. (i.e test results and specs)



Unless you define the problem with estimated  values as specs (dB)&amp;(Hz)  and the acceptable results, the solution cannot be defined.