I picked a flat weave wool rug off Overstock (or, I guess it's "O.Co" now). It's about 2.7" by 10 feet, which left me about 12" of length. It's flipped over the top step here and I think I might secure it down and leave it rather than try to cut the wool. I also used some carpet padding on each step for softness.
As you can see, I used a staple gun to nail this baby down. Just keeping it real around here. I'm going to add some black-finish nail heads to hide the staples for a finishing touch.