PA-24 pilot reported engine roughness and vibration in cruise. Pilot diverted to make a precautionary landing.

Narrative

After normal run-up and take-off; we departed from ZZZ on Runway XX and continued the climb-out over the water (eastbound). Once over land; we leveled out and contacted ZZZ Approach since we intended to fly to the mainland of Florida and use the VFR Flyway northbound to ZZZ1. ZZZ Approach advised to contact ZZZ1 approach. We established communication them and were given a Squawk Code. When approximately 5 miles SE from ZZZ2; the engine made a noise; not loud; but it was noticeable. There was also vibration. It was obvious to me the engine could not continue to run in this condition. I contacted ZZZ1 approach and said I was having an engine problem and needed to land. They asked if I was [requesting priority handling] and I said I absolutely was. I'm not certain as to the exact sequence of events with the communication from this point forward as I turned over the radio operation to my Copilot. Oil started to appear on the windscreen. We were cleared to land on Runway XX. We landed without incident on Runway XX and the propeller stopped spinning. I continued to roll down the runway until I reached the next taxiway and then exited. Oil was leaking onto the ground.The problem with the engine is undetermined at this point but it was obvious the airplane was not performing properly; just from the sound. My passengers are both CFIs and we operated as a team to get the airplane on the ground safely. We never felt that this landing would be anything other than successful but even though we didn't discuss it; we all were apprehensive about landing at a military airport. In retrospect; I should have been clearer on my intentions by stating [request priority handling] when I knew that I was going to land.