Syncing my iPhone with iTunes restores music I previously deleted from the device
You will need to use the manually manage music and videos option - otherwise, as you've already experienced, a sync will restore the deleted music to your device.

Steps for doing this are available at this Apple Support KB:


  
  Connect the device to your computer.
  Open iTunes.
  Select iPhone, iPad, or iPod in the Devices list.
  Click the Summary tab and select "Manually manage music and videos".
  Click Apply.
  Even when you have enabled manual management, you can still sync some content automatically. Select any content tab, such as Video, to enable automatic syncing for that type of content.
  


Another KB shows how to use this option to sync music for an iDevice with multiple computers. It also shows a picture of the screen that you'd see: