An Air Carrier Captain reported loss of oil pressure in one engine caused them to shut down the engine and divert to a nearby airport.

Narrative

While en-route from ZZZZ to ZZZ [Airport] at FL340 the First Officer (FO) (Pilot Monitoring (PM)) and I noticed that the oil quantity on the number 2 engine was indicating zero and the oil pressure was low in the normal range and was occasionally dropping into the amber for a few seconds and then back to normal. I transferred control of the aircraft to the First Officer and started the low oil quantity QRH procedure. This led us into the engine low oil pressure QRH. We did not yet meet the criteria to perform an intentional shutdown because the oil pressure was not in the red yet. I contacted dispatch via the crew phone app and had them patch me to maintenance to consult on the issue. While on the phone the oil pressure began to drop in and out of the red. We then discontinued the call to complete the QRH for engine shutdown. While on the phone dispatch did advise that ZZZ1 and ZZZ2 were the two closest airports and provided the weather at each. The weather at the time was rain in ZZZ2 and clear in ZZZ1 so I advised dispatch we would be proceeding to ZZZ1. We completed the QRH for engine shutdown and then advised ATC of the [urgent] condition. While I was on the phone with dispatch the First Officer and advised ATC we may have to divert and that we had the oil issue. He had also already looked at our single engine altitude. We requested FL220 and descended. ATC cleared us direct to ZZZ1. In the descent; I completed the QRH for one engine inoperative landing and the Non-Routine Landing Considerations. I advised both the cabin crew and the passengers we would be making a precautionary landing in ZZZ1. I then took the flight controls back from the First Officer.We continued to ZZZ1 and requested vectors to the ILS XX. We conducted the ILS in VFR conditions to a landing without incident. Safety vehicles inspected the aircraft on the runway and escorted us to the gate. Once at the gate we contacted Dispatch and maintenance to advise them of our status. No significant factors other than a loss of oil. No suggestions for the event however coordination of the deadhead flights for the crew was a bit scattered. Just better coordination between the Chief Pilots and scheduling on the status of the crew. In addition I was given almost this exact scenario on my Line Operating Experience (LOE) for my type ride as a Captain and that experience was very helpful in this event.