C172 flight instructor with student reported a loss of engine power while maneuvering. Flight instructor flew to nearby airport and landed safely.

Narrative

Flight Instructor and student were practicing the maneuver of power on stalls (which simulates stalling in the take-off configuration); located 10NM east of ZZZ. Upon recovering from the power on stall maneuver; and climbing back up to 3000 feet from 2700 feet; the student and myself started to feel the aircraft engine sputter and we saw a significant loss of RPMs which was around 1700RPM. CFI observed the temperature (located on the overhead vent) and it read 76 degrees Fahrenheit; based off of the gauge. We started to perform the engine failure procedure to troubleshoot the problem; and it was unsuccessful. We [requested priority assistance] with Approach; maintained our best glide speed of 65KTS; and tried to climb; but the aircraft performance was very poor. The RPM settings were altering between 2300RPM; 2000RPM; 1800RPM with full power being used; and it went back to 2100RPM; and kept repeating the same cycle. We communicated with ATC and they asked about the souls that were onboard; and how much fuel we had onboard; and what type of emergency that we were experiencing. We proceeded to follow a road; just in the event that we had a complete loss of power; and had to land the aircraft on the road. We kept the carburetor heat on coming in to land just in case there was carburetor icing. ATC had us land on runway XX; while XY was being used just to make it easier for us and we were able to taxi back to the ramp safely. We had approximately 26 gallons of fuel when ATC asked upon landing and we inspected it and it had 34 gallons of fuel and 7 quarts of oil. We also drained the fuel and it had no water contamination or sediments in the fuel tanks.