This question is more specific than other answers have given it credit for. Consider:
What would the size of a ring have to be to orbit a black hole, staying structuraly stable. The size of the black hole would be stable (not growing) and being the size of an intermediate-mass black hole.
This puts a definite range on the mass values of the black hole. This range starts well above the mass of our own sun. Stars over 3 times our sun's mass can turn into a black hole, but smaller than that, we haven't conclusively discovered any natural process than can create such a black hole.
Furthermore, if you are being actually literal with the definition of "intermediate", that means we start the scale at 100 solar masses.
The question also clearly specifies that this is a Niven-style construction. As such, the walls need to be high enough to hold in the atmosphere. Earth sea-level parameters give a characteristic height of about 8 km, and pressure falls off exponentially, so the radial dimension should be on the order of 50 to 100 km.
The event horizon of a 100 solar mass black hole would be at about 295 km radius. The photon sphere is the closest that you could orbit. It is an unstable orbit, but we can allow for active stabilization and control systems and easily wave this off. After all, the same was claimed from the original Ringworld concept!
At the photon sphere of our smallest intermediate-mass black hole (100 solar masses) will have tremendous tidal forces, and a 50 km structure is unworkable. Because of this, we would have no choice but to locate it at a more distant radius. But what accelerations can the wall tolerate? I'll say 1 g as a Fermi estimation to set the magnitude. Applying Newtonian tidal estimation:
$$ \Delta h \frac{ G 100 M_s }{ r^3 } = 1 g \\
r = 407,000 km $$
This is fairly nearly the distance between the Earth and the moon. This is the minimum radius for a ring which can withstand the tidal forces of an intermediate mass black hole.
That answered the question, but as the saying goes, there is a fly in the ointment. In doing this calculation I actually undermined the construction principle of the Niven-type Ringworld. In that design, we have unobtanium to hold against 1g of acceleration over a large radius. In the scenario I analyzed, the tidal forces alone are enough to produce Earth gravity over the scale of the walls. And this is true if you're in freefall orbit in the first place (actually, that changes the calc by a factor of 2 I think).
The logical thing to do would be to simply trash the unobtanium in the first place. You could get gravity by the tidal forces, so if this was a bike tire tube, you could live on the innermost circle of the tube or the outermost circle of the tube. You could even transit between the two, passing through zero gravity. Or, if you didn't want a full enclosure, you could expand the dimension to >100 km and have the space between the two surfaces unpressurized. This is fairly workable with conventional materials. Although, for this design you might need smaller tidal forces and, thus, a larger radius.
You don't even need a ring at all. The principle would work just fine for two space habitats held together by a tether.
But then you have other problems, like the lack of a sun to provide energy. I don't see any easy answer to that. There are some ways to get energy out of a black hole, but I these tend to focus on electricity production, and light production would necessarily be artificial.