How to politely ask someone to please be quiet
Well, avoid the exclamation mark.


  
  請保持安靜!
  Please keep quiet!  
  安靜!
  Quiet!
  小聲點!
  Lower your voice!
  請小聲點!
  Please lower your voice!
  


These from the above are a little commanding in tone, especially the second and third. You may change the tone by switching to a request rather than a command.

能否請你安靜 is relatively better. I usually go with this: 


  請問可以小聲點嗎? 謝謝。