Put a baby gate at the third step from the bottom of the stairs. Hide upstairs and call the dog to you. He will be able to go up the three stairs because he does not feel he will fall. However, he won't be able to come past the three stairs, so his fear response won't be reinforced. Come down to him and put the baby gate up three more stairs and go back up and call him if he hasn't already climbed them. Keep on doing this, and treating him with love and soft words, and soon he should lose his fear of falling. Hopefully. :)
Source: earthclinic.com pets section
By Robyn Fed from Hampton, TN
Great tip! For smaller staircases, you could also try this:
We once had a rescue boy who came to us also terrified of stairs, and the dog railed against any kind of gentle coaxing; the DH rigged up planks over the stairs to make ramps. Since this dog loved playing ball, we rolled the ball down the planks and he followed soon after. Then we took away one plank and rolled the ball--and he still followed. And then went the other until he didn't care about the stairs any more, because his urge for the ball was higher than his fear level by then.
It only took two days; remember, though, that this was a short, eight foot, stairwell, and we used two four-foot pieces of planking. Any flight of stairs longer than this, or very steep, may not work with this method. Both the OP and our methods really have psychological basis, they are a form of cognitive therapy, not unlike what docs will urge humans to do in order to face fears.
