Flight Instructor with student reported engine oil pressure malfunction during cruise. Flight diverted to safe landing.

Narrative

Night VFR flight with commercial student pilot from ZZZ1 to ZZZ. We noticed low oil pressure approximately 70 miles west of ZZZ2. Oil annunciator light was flickering; and that was when we saw oil pressure was in the yellow arc. We went through troubleshooting the issue with reference to the POH; and alerted ATC of the problem. The oil annunciator light then went from flickering to a steady glow; which then my student and I decided to [advise ATC]. We [advised ATC on] XXX.XX ZZZ center. We then corrected to divert to ZZZ3 and overfly the road in the event that we had total engine failure we would have a set place to land. We were informed by ZZZ Center that ZZZ3's runway was closed per NOTAM and ZZZ4 was the next closest option. The oil pressure had steadily continued to decrease since our first indication; at this point we made the decision to [request priority handling] to ZZZ Center. We were handed off to ZZZ approach where we were given a bravo clearance after requesting to remain at 9500 feet until ZZZ4. Upon reaching ZZZ4 we circled down and had an uneventful landing. The oil pressure had little to no reading at the time of landing.