Wow! I have the perfect cork floating floor that can be installed over stairs. You glue down the planks to the stair subfloor. The colour is called "Sunny Ripple" and it would be a beautiful compliment to the stained wood banister and trim and black metal accents!

My other option would be "Gemwood" which is an African black wood mimic!

I would then install the Sunny Ripple bevelled edge product (same colour but with a bevelled edge to mimic a hardwood plank) as the "dark hardwood" upstairs

Cork would work, choose a color that is a shade mid-way between the color of the tile floor and the wood on the bannister.

what does the "nosing" look like with cork? I've heard cork has a short life span. Is that a concern on stairs?

Cork "nosing" is not something you want for this. It rarely comes in colours other than "cork board" and can be more expensive than the flooring on stairs (it starts at $8/linear foot and it is DEAD-DOG ugly!). Stick with an oak trim that is stained to a complimentary colour. You will never regret going with oak.

Cork's lifespan can and has been over 100 years! US Library of congress has a cork floor that is now 150 years old. It is the owners' lack of proper maintenance that lowers the lifespan of any wood floor. Salespeople are strongly to blame for cork's lack of up-keep! I've spoken to 100s of flooring sales people over the last 2 years and less than a dozen of them know how to "sell" cork let alone maintain it. Only 3 sales people knew how/when to maintain a cork floor!!! That's less than 3% of all cork sales have had proper instructions from the point-of-sale people. I end up "fixing" the problems of "other people's" cork. But I don't mind...I love cork and will help anyone save the cork they have! I might lose a sale but I gain a friend.

Ok, that being said, cork flooring on a stair is considered a "low slip" surface. Once it is installed, you will need to refresh the finish of the cork every 5-7 years. This is done by adding 1 coat of water based polyurethane over the factory finish. You would repeat this maintenance for the 25+ lifespan of the cork.

Please be aware that some of the high-end cork floors (read: $6-$12/sf) have "ceramic" finishes OR Aluminum Oxide finishes. The salespeople will TELL you it has a lifetime wear-through warranty, but the reality is they still show wear and tear - micro scratches and filming because of scratches. The Aluminum Oxide finish (which is a health hazard for the installers because of the dust) is the most expensive and can NEVER be refreshed. Once it hazes (and it will), there is NO FIX! But...you will never 'wear through" to the cork!

And Wicander's Aluminum Oxide/Ceramic finishes are NOT ALLOWED to be sealed...they can not go in kitchens or bathrooms or entrance ways!!! AND they require frequent waxing (every 6 months) to maintain the warranty on this "Life Time Finish".

Makes you wonder!

Paint the risers white. We did that (with oak treads - sorry, no help there!), and it looks really sharp.

You have a "captured staircase, that is, the skirtboards on the wall and below the balustrade are solid to the tread, not open, where you can see the edge of the tread and riser from the hall. The skirt, or baseboard of the stair system is already painted, so a painted riser would transition easily. I do think the transition from your wrought iron balustrade and oak bannister is a bit stark with the white skirt board. Depends on what the trim paint is in the rest of the area, doesn't it. We see a lot of white painted trim....consider the hall and stair as a separate area and paint the trim a different color...perhaps a taupe that will compliment your dark wood floors and new treads. If there is no millwork break between rooms, that is, traditional cased openings, the options narrow. The curved treads will need to be custom. Your hardwood flooring contractor can usually handle the installation. One issue in the use of engineered flooring is that the curved stairs will not happen. Real wood treads stained and finished to match are the only real option. Cork is not. If not, there are contractors that specialize in stairs, check your local listings, Yellow Pages actually still works!

Generally, any transition from tile to wood is a break in finish...that means that wood changes shape with moisture and season and masonry, i.e. tile...does not. There are some pretty sophisticated caulks out there that try to deal with the issue, more or less effectively depending on cost. Then you have to decide where the paint to tile transition happens...caulking is round by nature and wood and tile are square, therefore the paint to tile transition becomes more focal. So maybe no to tile risers?

Best of luck with your project! Let us know how it comes out!