One of the biggest problems with slippery stairs is the angle at which they are placed. Often the steps are slightly sloped downward. This is to prevent water from collecting at the back of the step. The problem with this is that when it is covered with ice and if you place your foot on the step, it slides forward. If you can, I would suggest changing the angle of the steps. To answer your original question, no, there is not a type of paint on the market that will eliminate the slippery steps. There is, however, a product that will give the step more traction. Remove the existing paint. After applying a new coat of paint, and before it dries, sprinkle some No SlipTM compound. This is a powder that contains both sand and glass. Once the paint dries, it will leave a rough, abrasive surface. It is somewhat difficult to keep clean, but it will provide some much-appreciated traction on the step surface and it works with any paint.