C172 flight instructor with a student reported engine power loss during cruise resulting in a diversion to nearest suitable airport.

Narrative

My student and I experienced a partial power loss while in cruise on a cross country training flight. We diverted to the nearest suitable field; ZZZ1 [Airport]; to make a precautionary landing. Upon initial power loss; I heard a 'pop' sound followed by engine roughness and sputtering. We had an engine monitoring display onboard and it showed that cylinder #2 was not working. We could still maintain altitude but we weren't sure how long the engine would keep running. Using our GPS and a paper sectional; we found ZZZ1 and immediately turned towards it. Once we found the field; I asked my student to find an ATC frequency that we could talk on. I asked him to find a frequency for ZZZ Approach because that was the closest Center. He told me he couldn't find the frequency so I tuned into ZZZ Center. I called up ZZZ Center and let them know our situation; they gave us a couple options such as ZZZ2 [Airport] which was 10 miles north of us. By the time this happened we were already over the ZZZ1 [Airport] and told them we were going to land to 'play it safe'. They also [gave us priority handling] and asked for some contact info. They gave us a phone number to copy and said we didn't have to call it. We landed safely on the east facing grass field and shut down. I was able to contact ZZZ Center via radio on the ground and let them know we were safe. An owner's friend came to check in on us. We were safe with no injuries or damage to the plane. He left about 20 minutes later and another local came to meet us.