First Officer reported cabin pressure was uncontrollable in flight. The flight crew reset the Cabin Pressure Controllers to manual and regained control; then continued to destination at a lower altitude.

Narrative

We had a normal departure and several minutes later ATC cleared us to climb to our cruise altitude of FL310. Passing through about FL200 I noticed a pressurization anomaly in my ears. We pulled up the pressurization ECAM page and noticed that the outflow valve was oscillating open and closed and the cabin rate was swinging wildly up and down. At this point we asked ATC to stop the climb as a precaution and they cleared us to level at FL220; which we did. At about this time we got an ECAM caution message 'CAB PR SYS 1 FAULT.' I noticed that the airplane automatically switched from system 1 to system 2; as was shown on the PRESS page of the lower ECAM. I was hopeful that the switch to system 2 would stop the uncomfortable cabin pressure oscillations; but there was no change. There are no ECAM actions for this message; and the follow up takes you to the ETOPS pages; which did not apply to our flight. In the anticipation that a system 2 failure may be imminent; I looked up that procedure. In a 'CAB PR SYS 1+2 FAULT' the first step is to select the Manual pressurization button and assume manual control. I suggested to The Captain that we should consider this; as obviously the automatic mode is unable to control the cabin pressure. After a short discussion he elected to contact Maintenance Control though Dispatch using the crew phone for advice. They didn't have any other info for us but mentioned that manual mode would probably solve the issue but they could not direct us to do that and it was up to the Captain. He did not want to go to manual mode so we continued on.We looked at our fuel situation and determined we had plenty of fuel to fly lower. We thought that a lower altitude may make the oscillations decrease and make everyone on board more comfortable. We asked for and received 17;000 ft.. Unfortunately the lower altitude did not help. In fact at this point we noticed we were more pressurized than normal. At 17;000 ft. the cabin pressure was -1;000 ft. and the differential pressure was 7.7psi. Below the limitation but still much higher than normal at that altitude. I continued to voice my opinion that we should select manual mode as both of the automatic systems were clearly not functioning properly and a descent was making things worse. The Captain stated that we were not directed to via the current ECAM so we would not.When we were on the arrival I mentioned that if we continue descending and the airplane continues to pressurize more; it will exceed the limitation and we will be in an over pressure situation. At this point The Captain agreed to try going to manual mode. We looked at the pressurization charts in the book for guidance and pressed the button. Instantly the situation became comfortable again. The oscillations stopped and we were able to manually control the outflow valve in both directions and the situation was completely resolved. We followed the manual pressurization guidance that was now on the ECAM and supplemental pages and made a normal; very comfortable approach and landing in ZZZ1. The discrepancy was added to the logbook and local maintenance notified. Despite only having an ECAM failure message for one system; it was clear that neither automatic pressurization systems was working properly so I encouraged the captain to fix the problem by going to manual; as the dual failure procedure directs. The Captain suggested that we both file reports because we selected manual pressurization mode without the ECAM specifically instructing us to do so. I agreed because while I think what we did was the correct course of action; there is always the possibility that despite our best intentions; we may have unintentionally or unknowingly broke a rule or procedure. Despite both of us searching our manuals; we could not find clear guidance on what to do in our exact situation. It would have been nice to have a QRH procedure for rapid cabin pressure oscillations without an associated ECAM.