B737 MAX Captain reported airframe vibration during climb. The flight crew completed the QRH procedures; then accomplished a diversion and landing.

Narrative

After 10;000 ft.; during the climb and acceleration from 250 kts.; a distinct airframe vibration became apparent. The First Officer (FO) and I assessed the situation and discussed possible causes. Included in this assessment were items such as Autopilot malfunctions; aircraft trim issues; APU door position malfunctions (we were in a MAX) and Engine vibration (the engine Vibration meters were stable at L- 0.3; R - 0.5). With these potential causes eliminated; we referenced the 'Elevator Tab Vibration' QRH. Our observations in the flight deck satisfied two of the three listed conditions and we enlisted the aid of the Flight Attendants which confirmed the third; which is that the vibration was felt throughout the aircraft; but strongest in the aft section.With that information; we followed the QRH; which resulted in a noticeable reduction in vibration intensity as airspeed was reduced. We determined that the nearest suitable airport was ZZZ. The QRH says 'consider landing at the nearest suitable airport' so the FO and I discussed our options; and given our observations; determined a diversion was the most appropriate course of action. We notified Dispatch; the Flight Attendants and the passengers of the need to divert and coordinated with ATC. We were cleared to ZZZ and landed uneventfully.The landing was performed in excess of published structural limits but less than max quick turnaround weight. We determined landing overweight using Captain's Emergency Authority was appropriate and briefed considerations associated with doing so. We also ran the brake cooling module in the performance data to confirm there would be no issues approaching the gate after landing. After arrival at the gate; I contacted the (Operation Control Center) to provide event specifics and entered two defects in the Maintenance log - one for the overweight landing and one for the airframe vibration.