BAT (and ‘regular’ clicker training) can easily be adapted to use with a deaf dog. Just use a what I call a hand flash (5-fist-5 toward your dog) in place of the verbal marker or clicker. You may need a tactile (touch) signal to click when your dog is not looking at you.
With BAT, that means you’ll be using the hand flash for the times when you’d use a marker or a tactile signal (like a touch to the tail or rump) in place of the clicker if the dog isn’t looking at you. Be sure to pre-train that!
Update: Check out the Deaf Dogs webinar in the Academy!