B737 First Officer reported during climb aircraft began a subtle shake followed by a right then left wing drop resulted in pilot descent which stabilized aircraft.

Narrative

Climbing through FL330 to FL370 I was the pilot flying with CMD B engaged; LNAV VNAV AT armed. Just past FL330 the aircraft began a subtle shake for approximately 10-15 seconds after which the aircraft began to drop the right wing. I disconnected the autopilot and corrected with approximately 1/2-3/4 scale deflection on the control wheel back to the left which resulted in the aircraft to enter a left wing low state. Finally correcting back to the right; the captain and I agreed to lower the nose and level off the vibrations subsided. Still hand flying I tried a climb once more to FL370; the aircraft once again began to shake and we agreed to descend to FL310. On the descent the vibrations stopped and I reengaged the autopilot in level flight; once level the CA assumed control of the aircraft to feel out the flight controls and could not replicate the unstable aircraft state. We agreed to continue to ZZZ and landed uneventfully.