I assume you can't get under the stairs. That would be the best, as
you can simply screw together the two pieces of wood rubbing against
each other and making the noise.
Second best is to cut a hole in the wall and crawl under the stairs to
do the same.
Okay, you probably have to go for option 3. Your local hardware
place/warehouse has a kit called "Squeeek No More." Try that.