This tip came to me via email.  Have not tried it yet, but it might just work.

Apply a glob of liquid soap to a cotton ball. Cover the tick with the soap soaked cotton ball and swab it for a few seconds (15-20), the tick will come out on its own and be stuck to the cotton ball when you lift it away.
 
This technique has worked every time I've used it (and that was frequently), and it's much less traumatic for the patient and easier for me. Unless someone is allergic to soap, I can't see that this would be damaging in any way.