CE500 Captain reported a stabilizer miscompare annunciation along with airframe vibration resulted in a diversion to a safe landing.

Narrative

On departure out of ZZZZ we retracted flap at approximately 800 feet AGL after takeoff. The STAB MISCOMPARE annunciator illuminated. I asked the FO to keep the speed below 200 KIAS and then we called for and complied with the appropriate checklist. Since the checklist called for keeping the speed below 200 KIAS since we couldn't not resolve the problem we elected to divert to our en-route alternate which was ZZZ1. We received this new clearance after explaining the situation to ATC. I called ops via airinc and explained the situation and informed them of the diversion. A few minutes later passing approximately FL200 at just under 200 KIAS an airframe vibration developed. We decided at that point that we would divert as I did not know if the aircraft was damaged. I asked airinc to inform my company and we diverted to ZZZZ2.I elected not to use flap for landing as I was unaware where the vibration was coming from and did not want to change the configuration which could have worsened the problem. We completed the appropriate checklist for a flapless landing and after some radar vectoring to burn off excess fuel (to avoid an overweight landing without flap); we landed without further incident.