Pilot reported engine failure and diverted to the nearest airport and landed safely.

Narrative

At cruise at 5;500 ft. en route from ZZZ1 to ZZZ2; engine began coughing and running rough; immediately I put the mixture rich; and when that did not seem to help; I ran the checklist for losing an engine. I first noticed my oil pressure was low. I ensured the fuel was running from both tanks. I pulled the carb heat. I switched the magnetos to left; then to right. then I recycled them completely. As the engine kept running rough; I [requested priority handling] with ZZZ Center and squawked 7700. The Controller advised of the airport ZZZ to the east and off my right. with the power full forward; the airspeed was holding 90. Upon spotting the airport; I entered the downwind with altitude to lose; and pulled the power back to 1500 rpm; the engine died completely. I made it to the ground and landed safely; engine sputtering slowly as I rolled to the only vacant tee on the Ramp. Another aircraft was on the field's CTAF relaying for ZZZ Center. I told him I was on the ground and that I would contact ZZZ Center when able; I did such later that evening through the FSDO.