McDonnell Douglas pilot reported engine failure during climb out. The Pilot performed an in flight shut down and diverted to make a precautionary landing.

Narrative

During the climb to 7;500 feet; on passing 7;000 feet; number 2 engine started vibrating and produced black smoke from the area of the gills. The engine was throttled back and the aircraft leveled off. The departure airfield; ZZZ was relatively close so a 180 turn to the left was carried out and a slow descent initiated in anticipation of a landing. The smoke from the engine had now turned white. All engine indications at this stage were still normal. Runway XX had been used for departure at ZZZ. Work was taking place on the runway and it had been open to allow the departure. Center was asked if they could confirm if Runway XX would be available. They came back saying it closed and would not be available but suggested ZZZ1 which was closer and at 1;500 meters; sufficiently long. At this stage the oil pressure started to drop so the engine was shutdown and feathered. The decision to divert to ZZZ1 was taken and approach was flown to a safe landing. It was not possible to taxi clear of the runway so the aircraft was shutdown and towed.