You really should take people's advice here.  Passing a polygraph (which you may be able to do if you correctly use CM's) won't be the best thing for your relationship.  She's obviously hurt by what you did and continue to do (not judging, but based on your post you admint to lieing and she demands a polygraph to see if you are truthful).  She obviously thinkd what you've done is pretty serious.  

God luck working things out with her.  But I'd stay away from a polygraph.  Even if you pass, what does it really prove?  If your relationship is at the point where you are lieing and she is demanding a polygrpah, passing a polygraph won't help.

So my unsolicited advice:  (echoing anxeity guy) "DON't TAKE THE TEST"
and..
STOP LIEING TO HER (if you want a healthy relationship)