I'd expect all but the very smallest toy breed dogs to handle stairs fine, and even then it may be more of an individual thing than the whole breed. Some chihuahuas, for example, are only six inches at the shoulder as adults and really incredibly tiny - I'd be concerned about them going up and down long flights of stairs, or having access to staircases when they're home alone, if only because if they fall they could be hurt much worse than a larger dog would be. But I doubt I'd worry about a couple stairs on and off a front porch, for example. Other chihuahuas might be more than twice as tall and at much less risk of injury on stairs. Assuming there aren't health issues complicating matters, of course - bad knees, back injuries. etc. may mean stairs are a problem for any dog.
All growing puppies of any breed and size should have limited access to stairs and avoid running up and down them unnecessarily, because it's a high impact exercise that could negatively impact growing joints. So that should be taken into account if you're planning on getting a puppy.