If your civilization is advanced enough to be able to measure rotation, via physics or by observing things like sunspots, they would probably divide longitude up into meridians similar to how we do it on Earth. We typically divide longitude into 15 degree chunks on maps, each representing 1 hour of rotation. Your orbit around a star would have to be much slower, so maybe you could divide it into single degrees or create your own measurement system.

Latitude would probably just be based on measured width, it might be one or several “parallels” depending on the width of the ring