Pilot reported engine vibration while in cruise. The flight crew requested completed a diversion and precautionary landing.

Narrative

Flight was going smoothly from ZZZ1 to ZZZ2; as soon as we passed ZZZ at 9;000 ft. The aircraft started shaking moderately; like something was wrong; not as if we were in turbulence. Person A took the controls and then disengaged autopilot. I pointed out that cylinder 2 seemed to be out. He asked me to find the nearest airport; I told him it was ZZZ and how far back from us it was. He then diverted from our flight plan and hesitated before telling ATC we were diverting for engine issues. There was a loud clanking sound that seemed to be coming from the engine block area or below it. I could tell Person A was becoming task saturated because every response to ATC was talking a while; I took over all comms after that. I talked with Approach. Letting them know it looked like we lost a cylinder. That we were a single engine aircraft and how many souls and fuel was on board. Person A handled all the flying. I pulled up the engine page and kept reading him any difference in readings. Cylinder 4 appeared to have been lost as well; soon there after starting our descent. Person A kept power in as long as possible (he later said he was nervous of reducing power and not being able to get it back). He then asked me to run the checklist. I tried finding something on the QRC lists that would match up but nothing did. So I went through engine failure and nothing on that helped. (Person B asked Person A if we ran the partial power checklist; we did not. It is only found in the POH and I hadn't seen it before and Person A could enunciate what it was for me to look for it) I asked Person A if he wanted to squawk XXXX and [request priority handling]; he said no. They cleared us into ZZZ and at that point we still have thousands of ft. to lose. Person A asked to circle to lose altitude; ATC said yes and he still had power in. I suggested he take power out to start slipping and losing altitude; I don't remember if he did or didn't I just remember having to do a 2nd 360 to lose more altitude. At some point in this descent all the EGTs went cold on the engine page. ZZZ Tower asked us if we wanted emergency vehicles waiting; I asked Person A and he said yes; so I asked again if he wanted me to squawk XXXX and he said no. Once we went idle on our final into XXR and he added like 15% power at short final; the cylinders all came back into the green around the same average. He landed safely and we asked to taxi to the run up area to see what was wrong with the aircraft. We called Maintenance and spoke to Person C; I explained what happened and he said he was suspecting a fuel line clog or a sensor issue. They had us run up the plane at full power to clear out any blockage. They suggested we turn the plane off for a few hours to let it cool off and do the run up again. Person A called Person B and he figured out he was no longer legal for the day. They expected us to fly down to ZZZ2; because on the Maintenance from the information we gave them; there is no longer anything wrong with the aircraft after our sunup at night and again the next morning and us doing 2 touch and go laps at the airport.SOPs should be followed at all times not just when its convenient and cost effective for the company. We followed our SOPs and landed immediately; technically that plane was 'squawked' but Person A didn't squawk it officially until we reached ZZZ2. A plane that showed a defect whether it is assumed to be a sensor issue or not should not be flown until seen by a mechanic. It seems very irresponsible of the Company to ask us to continue in a plane without confirming it indeed was nothing critically wrong. What's the point of following SOPs if admin and maintenance will ask us to fly the plane the same or next day; because we don't have someone contracted at the diversion airport to take a look.