B737-800 First Officer reported a medical emergency inflight.

Narrative

During cruise; #1 Flight Attendant (FA) had called the fight deck to inform us that an elderly passenger was having difficulty breathing. I was given command of the aircraft and radios while the Captain communicated with dispatch via the Application. We were instructed to have FA's seek medical assistance. After a short period we were advised by the Flight Attendants that 3 of 5 oxygen bottles failed to operate and that the passenger would not have enough oxygen to make it the remainder of the flight. During this time the passenger was being attended by a physician on board. The passengers situation was improving but then quickly deteriorated. At this time; the physician on board communicates that we need to divert; and quickly. The Captain informed Operations Control and Dispatch and the mutual decision to divert is made. ZZZ is agreed upon and I was instructed by the Captain to [request priority handling] and divert to ZZZ. We maintained maximum safe forward speed and got on the ground as safely and practically as possible. Due to our load; we anticipated an overweight landing. While I managed the flying; the radios and coordinated with ground personnel; the Captain accomplished the applicable checklists. Upon completion of the checklists and briefing the controls were transferred to the Captain and he made the landing and then taxied to the gate. The passenger was removed via paramedics; and we communicated with dispatch and maintenance.Although its not known if the passenger would have made it to ZZZ1 with all O2 bottle operational; it limited time and diversion options. Unfortunately a medical diversion is unpredictable. I commend the crew for handling the situation as professionally and expeditiously as possible regardless of the challenges encountered and adapting.