If we can't refinish the stairs then this might work. DIY: How To Cut, Paint & Install Stair Treads + How To Remove Carpeting + How To Install A Stair Runner (awesome step-by-step tutorial & pictures!) - these are excellent tutorials!
stained wooden boards with a dark stain - placed doormat on top - then sprayed over all with 4 light coats of creamy colored paint. When you remove it the stained wood that was covered by the mat leaves a beautiful design.