I had the same problem.  They hate anything sticky, so I bought a roll
of wide clear packing tape.  Fold a 2'length in 3 so that it sticks
onto itself (it should look like a long thin tube now). Stick one to
the edge of each stair. You might catch the odd one on your socks when
using the stairs, but it's easy to make another one. Leave it on until
he's trained to use a nearby scratching post.  Praise like crazy when
he does it right!

YES Amonia.

Does your cat have many other places to scratch, like cat trees, sisal
posts, carpeted posts, or corrugated cardboard?  He needs to be provided
with several places where he can scratch.

Sticky Paws is clear adhesive sheets formulated to stop scratching on
unwanted areas.

For our four cats, we have two large carpeted cat trees, two medium
carpeted scratching posts, and two Smarty Kat Super Scratchers (corruagated
cardboard - very cheap, $10 at Wal-Mart.)  With the introduction of each
cat the household, if we saw them scratching on the couch/carpet, etc, I'd
simply say, "NO," then pick them up and take them to an approved scratching
location.  I then show them how to scratch and move their paws to scratch
on it, then praise them lavishly when they did and give them a treat.
After a few times of doing this, they no longer scratched anywhere else
except their approved places.