Vibrato can be hard. Check out this book, Playing The String Game by Phyllis Young. She has some great suggestions on fun games to play to get your students on the right track.

I tell all my students that they need a few prerequisites regarding how they hold their instrument before vibrato will work at all.

With vibrato, there are 3 points of contact from the instrument to the body.

1. Thumb to neck of instrument (thumb MUST be loose and not "grasping" the instrument)
2. The finger being vibrated (this finger must be tall, and only the tip of finger on the instrument)
3. The chin/shoulder on the instrument.