PA28 instructor pilot; with trainee; reported the engine began to run rough during cruise flight.

Narrative

During cruise; the aircraft's RPM unexpectedly dropped from 2300 to 1700. At this point; I; the second-in-command (SIC); took over the controls from the PIC; who relinquished them. The following troubleshooting steps were immediately taken:Carb heat was appliedMixture set to full richFuel pump turned onFuel tank was switchedAfter these corrective actions; the RPM returned to 2300; and the aircraft stabilized. I immediately communicated the situation to ATC; stating:'Approach; aircraft x having some issues with the RPM; they are fluctuating; I'm not declaring an emergency.'ATC acknowledged the situation and asked for my intentions. I informed them that the aircraft was under control and that I was not declaring an emergency. I requested to divert to ZZZ. Approach continued to provide guidance; and I began a descent at my discretion.The airport was in sight; and I was cleared for the frequency change to ZZZ tower. I informed ZZZ tower of the situation; and they asked if any assistance was required. I confirmed that the aircraft was operating smoothly and no assistance was needed.Landing and Post-Flight:A safe landing was completed at ZZZ and we taxied to the FBO where the engine was shut down. The aircraft was found to be operating normally at that time.Following the incident; I contacted our Director of Operations; who advised us to secure a hotel for the night due to the late hour and instructed us to return to the airport in the morning for further inspection.Morning Inspection:The next day; we contacted the Director of Operations and were advised to perform a run-up with the assistance of an AMP (Aviation Maintenance Professional). A pre-flight inspection was conducted; and all parameters were found to be within standards.We performed the run-up three times; each time finding no anomalies; and the aircraft's systems operated normally. Due to the inability to replicate the RPM fluctuation; it was decided to proceed with a return flight to ZZZ1 under IFR; though the flight was conducted in VFR conditions for the duration of the return trip.Conclusion:The flight was conducted safely; and the situation was effectively managed. At no point was the situation deemed an emergency. The aircraft is operating normally post-inspection; and no further issues were identified during the subsequent run-up checks.