My personal opinion is that you're asking for trouble adding a bunch of intense herbs to a juice fast. The body, and particularly the liver, has enough to do without throwing extras at it. I would stick with juice.
And I think it would be foolish to drink coffee during a cleanse. Caffeine is one of the items we are looking to relieve the body of, to detox, during a fast!
That said, I would NEVER stop drinking that coffee cold. Taper off over three days or so before stopping or risk the mother of all headaches. Been there.
Have a great cleanse and remember: FLUSH FLUSH FLUSH! Drink lots and lots of juice, water, mild herb teas... and reap the results.