SR22 Flight Instructor reported engine roughness and a knocking sound coming from the engine while in cruise flight. As the problem got worse; the flight crew opted to safely divert at a nearby airport.

Narrative

Prior to departure from ZZZ; during the run-up procedure; we noticed a slight roughness upon checking the right magneto. We proceeded to go through normal spark plug cleaning procedures; and the following check displayed no roughness; and an RPM drop well within standards for departure. We elected to depart; headed for our destination of ZZZ1 via ZZZ VOR; to avoid the active restricted airspace. This route of flight unfortunately did not provide an overabundance of suitable diversion airports. Roughly 15 - 20 minutes into the flight; we began to hear a slight 'knocking' - best descriptor I could think of at the time - from the engine; every few minutes. We noticed the issue; and started with changing our mixture slightly to hopefully find a position the plane liked more. As we continued on our route of flight; the abnormality got slightly more frequent. At this point; we began more intense troubleshooting procedures aligned with checklists; and advised ATC of our new intention; which was to divert to ZZZ2; which had a Cirrus Service Center for maintenance on the ground. At this point; the abnormality was still fairly spread out; and not severe. ATC asked if we were requesting priority handling with the diversion. I advised them that; at that moment; there was nothing indicating that was necessary yet. Shortly thereafter; the abnormality became much more frequent; and more severe. At this time; I elected to turn around to ZZZ3 airport as the closest runway; and request priority handling with ATC as a precaution; in case the problem became worse to the point of failure or severe loss of power. ATC was extremely helpful in this situation; and operated exactly as intended in such a situation. I maintained altitude until over ZZZ3; and by the time we were over the airport; the abnormality was frequent enough that it seemed constant; and fairly severe. There; I circled over the runway to descend; staying slightly high on final and performing a slip maneuver to ensure glide range to the threshold at all times. We were able to taxi to parking under power. Upon shutting down the aircraft; I immediately called ZZZ Center as instructed to advise safe on the ground; with no injuries or assistance needed. As a final note; I was well rested with 12 hours rest time; within duty day and flying/instruction hours; had eaten breakfast; and was not in any negative emotional state. IMSAFE checklist was all met well above what was needed.