Can't get vinyl on stairs or 2nd floor?
Your saying vinyl, but I think you really mean laminite instead.
There is not good way to lay laminite on a set of stairs. It's a floating floor, how would you trim it out on the ends and over hang and still have it move?
At the top of the stairs you have to have a landing tread, a landing tread is 3/4" thick, how to plan on making the transition from the tread to the flooring?
Laminite is also loud to walk on unless you go with cork underlament, all that sound will be transmited down stairs.
Some condo associations ban the use of it for this reason.
Far better to use real wood stair treads and at least engineered flooring if you want a real wood look.