How can I stop Google Play Services from updating automatically?
If you've unlocked root, there's another option. You can move the latest working GMS (10.0.84) to system partition and block auto-updates by creating empty folders with the APK name.
  
  KitKat (tested):
  
  · APK goes to /system/priv-app/com.google.android.gms.apk
     · libs go from /data/app-lib/com.google.android.gms-{1, 2}/  to /system/lib/
     · mkdir /data/app/com.google.android.gms-1.apk /data/app/com.google.android.gms-2.apk
  
  Lollipop+ (presumed):
  
  · APK goes to /system/priv-app/PrebuiltGmsCore/PrebuiltGmsCore.apk
     · libs go from /data/app-lib/com.google.android.gms-{1, 2, 3, 4}/  to / system/priv-app/PrebuiltGmsCore/lib/arm/
     · mkdir /data/app/com.google.android.gms-1.apk /data/app/com.google.android.gms-2.apk /data/app/com.google.android.gms-3.apk /data/app/com.google.android.gms-4.apk


(posted this on the »Google Play Help Forum« thread earlier)