B737 First Officer reported loss of engine oil pressure requiring inflight shutdown and diversion.

Narrative

Approximately XA20 enroute to ZZZ at FL340; I noticed a fluctuating oil pressure indication of the number 2 engine with a zero-quantity oil indication and informed the Captain. Shortly after; I assumed control of the aircraft and radios; while the Captain started QRH procedures for Engine low quantity.During the QRH process; I informed ZZZ Center of an impending engine shut down due to loss of oil pressure and will keep ATC advised; I also used the FMC to calculate an engine out drift down altitude of 22;000 ft. The Captain then reached out to Maintenance Control for guidance as the current aircraft conditions did not meet QRH procedures for a precautionary shut down. During this time; Captain has asked me to start looking for a diversion airfield; I referenced Jeppesen charts for suitable fields and after asking ATC for help in obtaining the current weather and runway in use; I elected ZZZZ as the prime candidate since it also had medical and company presence. Shortly after; we resumed QRH procedures as the oil pressure indications continued to drop from amber to red; resulting in an inflight shutdown. The Captain and I agreed ZZZZ was the best suitable; and after coordination with dispatch; the captain [requested priority handling] and we changed routing to ZZZZ. ATC cleared us to descend to 22;000 ft. initially and I trimmed the aircraft for the descent and slowed the aircraft to 280 kts. to give us additional time to complete all checklists; I also set up the approach in the FMC while the Captain addressed the cabin crew of the issue and informed the passengers of the diversion.After the Captain finished his tasks; I informed him of the speed; and trim setting and transferred control of the aircraft to him; we also briefed the approach (flap override; higher descent rate; go-around considerations etc.) As the aircraft descended lower; I called the cabin crew to check if all is fully seated; cooled the cabin further and briefed them on ETA and flight conditions.Upon contacting ZZZZ Approach/ATC; we were given a different approach and unfavorable vectors; we requested the ILS XX and informed them our intentions of widened and delayed turns. The aircraft was stable on the path outside the FAF and landed with a full stop on the Runway. While the Captain addressed the passengers over the PA; I informed ATC to let emergency vehicles approach and inspect right side of the aircraft. After we received the thumbs up from Airport Rescue and Firefighting (ARFF) ground personnel; we taxied the aircraft to the gate and deplaned the passengers. After approval from the Chief Pilot; we returned to the flight deck and assisted ground personnel in towing the aircraft off the gate; to parking it at an Apron and shut it down completely. I was well rested for the sequence and was alert; the Captain was great in directing and keeping everyone informed. The flight deck and cabin crew had excellent CRM leading to the safe outcome of the flight. QRH dictates to verify Oil pressure to drop below red line before proceeding to inflight shut-down; the time it takes can delay decision making. I believe pilots should be able to monitor and proceed with pre-cautionary shutdown before red line is reached.