When a coil is wrapped around a ring of non magnetic material, is the path length (l) the circumference or the diameter of the ring?
The length in question is the path along which the magnetic field travels. Given that you have described a circular solenoid (unless I'm mistaken) then the mean circumference is the length you need to use in your equation when calculating magnetic field strength, H.



The dotted line marked B (flux density) travels along the mean path length = \$2\pi r\$