There was a thread recently by someone who had painted her stairs and used cork underlay as the grips. She said she didn't use any sort of glue or adhesive, just cut it and placed it (unpainted side down) to fit the stairs. She said both humans AND dogs had been up and down it with no slippage at all. If I can find the thread, I'll try and link it. Obviously, it won't be a decorative solution but if you just want it for the usage factor, this could be an option.

Here it is: [Painted Stairs[(https://www.houzz.com/discussions/painted-stairs-dsvw-vd~587589?n=183)

Consider a carpet runner.

Thanks everyone...very helpful!

I uses carpet treads. These are from Colonial Mills and held on with their recommended Colonial Mills carpet tape. It is not supposed to damage the wood underneath. I haven't removed any so I can't say if that is true. They have been on a year. We have two small dogs.

Yes - the carpet tape holds the carpet tread to the wood. This is what I used:

http://www.amazon.com/Stair-Tread-Installation-Kit-N/dp/B00A2BR8LG/ref=sr_1_1?ie=UTF8&qid=1447818601&sr=8-1&keywords=colonial+mills+carpet+tape