B737-800 Captain reported an oil filter bypass condition and the decision to divert.

Narrative

ZZZ to ZZZ1; myself and my first officer experienced a mechanical event while in the cruise phase of flight. In cruise at flight level 370 our number 2 engine experienced an oil filter bypass light. As captain; I was the PF for this flight so my first officer ran the appropriate QRH. Following the QRH; it had us reduce the power; and this did extinguish the light momentarily. While the light was out we had requested a lower altitude from ATC because we were slowly losing airspeed and wanted to start a gradual descent while we worked through our problem and regain a positive airspeed trend. As we started the descent I transferred the controls to the FO so I could handle talking with my dispatcher over ACARS to coordinate a diversion airport. As I was heads down my FO advised me that the oil bypass light had reappeared and he was having to continue to reduce power to keep it out. I then continued to request lower from ATC for airspeed control. I had not received a response from my dispatcher over ACARS yet so after evaluating the situation with my FO and being familiar with the local area we were over; I exercised command authority and decided to divert to ZZZ2. Once we started our turn to ZZZ2 my FO had advised me that the light was now staying on consistently and he was now at idle power. I then readdressed the QRH which led us to an engine shutdown. This is when I decided to request priority handling and have trucks standing by. As my FO was handling the PF duties I shut the engine down per the QRH; ran the one engine inop landing checklist; and then proceeded to the non routine landing checklist. Once I was caught up my FO briefed me where we were in the terminal area and I then decided for him to remain PF while I briefed the approach and ran the decent checklist. We then transferred the controls back to myself as PF and ran the Before Landing. The rest of the approach was uneventful and led to a successful abnormal landing. After coming to a complete stop; safety personnel looked over the aircraft and advised us that our number 2 engine appeared to have an oil leak and some had collected on the engine cowl. With no other abnormality we decided to taxi back to the gate and have the trucks follow us for an uneventful taxi to the gate.Cause: Quicker response from dispatch. Once I had received a response we were already close to ZZZ2 for landing.