How can I couple relay chattering noise to a data cable?
Usually when people talk about chattering in a relay, they mean in the sense of electrical noise rather than audible noise.  When a relay closes, ideally it's a single, instantaneous switching action.  In reality, the relay will 'chatter' when the circuit closes because of contact bounce, worn contacts, etc.  There will also be noise when breaking the circuit because of sparking between contacts.  Here's a video from Dave of the EEV blog describing contact chattering and the methods for overcoming it from a signals processing standpoint. https://www.youtube.com/watch?v=Nj-Q8FQxHhU

For a relay's typical use, as a rarely-switched power device, relay chattering is usually inconsequential.  For example, the (resistive) broil element of an oven does not care if there's a millisecond of electrical noise when the relay is switched.  

However, a data line should not have spurious noise.  In addition, relays are not meant to be rapidly switched!  The contact is usually driven by an inductive coil (which resists rapid switching) and the contacts are worn down by the switching action.  If you want to drive a data line, use a transistor instead.