Rain happens when the pressure of moist air drops enough to form droplets and the droplets get heavy enough to fall.
The trouble that I see is that the pressure will probably drop off slower than the "gravity" (which is opposite the situation on Earth).
There is no actual gravity in a spinning cylinder. The cylinder spins and the tangential momentum from that spin, pushes you into the cylinder.
If there was no atmosphere in the cylinder, there would be no "gravity" if you were not in contact with the surface. With an atmosphere, the atmosphere, through friction from the inner surface of the cylinder, gets dragged into the spin. The spinning atmosphere provides a lateral acceleration that pushes toward the surface of the cylinder. It only seems down because the surface is rotating in the same direction you are being pushed (the surface will move faster so you will fall "down" anti-spinward).
Since the spin (thus perceived gravity) decreases as you move toward the center, I'm concerned that any droplets that form near the center will not be pushed toward the surface.
So, how would we get "natural" rain in a spinning cylinder? I'm assuming a 1km radius but that is open to change.
The solution must allow clear air for the first 100-200 meters from the surface. So, super saturated moisture is likely out (we gotta breathe and live in there).
If possible, I would like to do away with the need to spray fake rain.
While it would be amusing, I would also prefer to avoid bucket sized drops plunging from the center.