I've had tonsil stones since I could remember! I've never gagged or got sick from them though. I have, however, accidentally swallowed a few and I'm surprised I didn't throw up from the disgusting taste. But I digress. What I do is I gargle with some warm salt water for a few minutes and use a qtip to gently push them from my tonsils then I spit them out. They say good dental hygiene gets rid of tonsil stones but I take really good care of my mouth and I still get the buggers. The salt water really helps though. Give it a try. If you're worried about gagging when removing the stones, hold your thumb with your other fingers (picture below) and that may help.

http://i.kinja-img.com/gawker-media/...xen46ibjpg.jpg