B737 Captain reported a vibration while accelerating and climbing to FL310. Captain diverted and landed safely.

Narrative

Reassigned to fly ferry ZZZ-ZZZ1 due to ZZZ2 weather/ATC delays. Original departure was XA:45 with actual push at XH:36. During climb and acceleration above 250 knots noticed a vibration that seemed harmonic at times and decreased slightly in intensity with deceleration from .792M to .76; but did not completely subside. Tried FL310 and 330. Slowed to .77M. Phone patch to Maintenance Control via Dispatch; continued with no change. No lights in the overhead; no abnormal engine indications. Only abnormality was a reading on the right ELEV in the manual reports in the DFDMU (Digital Flight Data Management Unit) menu under FLT CNTL page 2 that showed over -5.0 on the right side and around -2.0 on the left. Checked FM (Flight Manual) for non-normal and ran ELEVATOR TAB VIBRATION checklist. Vibration subsided at 230 knots at FL190. Deduced possible issue with the R ELEV and took the 'advice' of the NON-NORMAL checklist to land at nearest suitable airport ... ZZZ3. Divert to ZZZ3 and [advised ATC] due to flight control malfunction that allowed us to stay at 230 Kts maximum inbound. Uneventful landing and taxi to gate. Met with flight operations service coordinator and ZZZ Maintenance on aircraft. Full debrief; and ELB (Electronic Log Book) entry. Advised of requirement for a VIBRATION REPORT by ZZZ Maintenance via flight operations service coordinator by phone after we arrived in ZZZ to wait for our pairing to update. [Chief Pilot] notified of EMERG/DIVERT; and patched me to Maintenance Control. Requested the form via EMAIL. Unable to print; from IPAD so I answered the questions in an email back to the Maintenance Control rep who had pushed me the request.