How to disable iOS FaceTime notification sounds?
I found this extremely frustrating as well. I spent an hour trying to record a silent ringtone in GarageBand but it consistently delivered noisey ringtones despite no sound on the track. I was about to give up when I thought someone else besides us must have been annoyed and figured it out. A Google search yielded the silent ringtone below. I tried it and it works great. Good luck.

http://www.codingmerc.com/blog/silence-ringtone-available-for-download/