To find out what stairs you can currently challenge someone in, first go to the Main Stairs Page, then click on "Show your stairs only" link. The ones in BOLD are ones you can make a challenge in. .
Fencer: How about an indicator on the page where you can view all the stairs you are currently playing in, that would allow you to see which ones you have to wait before you can challenge in? That way you wouldn't have to go to the individual page for each to find out if you can issue a new challenge - you'd be able to tell at a glance from the "show your stairs only" page.