B737 Captain reported #2 air conditioning pack control problems in cruise. The flight crew elected to divert and make an uneventful landing.

Narrative

I was Captain (CA) and Pilot flying (PF). Aircraft was on pre-existing MEL for one of the two control channels of the right AC pack being INOP. During cruise phase the right pack tripped off. No cabin pressure anomalies were noted. Followed QRH procedures to reset & restore right pack normal operations. Which were successful for only a minute or two then the trip recurred. At which point we followed QRH guidance for an non resettable trip; which amounted to turning off that pack and proceeding single pack. We discussed continuing or dropping into ZZZ which was then a couple hundred miles ahead of us. We were both slightly against proceeding as to this flight; but were more concerned about delivering a broken airplane to ZZZZ for the return flight than we were for our own situation. Elected to contact Dispatch & Maintenance Control for advice. Swapped PF/PM roles so CA could concentrate on admin while First Officer (FO) flew. Asked FO to prepare mentally and set up the aircraft for a divert to ZZZ in case we went that way. Had no success with the crew phone system using either pilot's iPad. From the sound of the audio distortion it appeared we simply did not have the bandwidth for voice traffic when competing with all the other traffic from passenger use of the internet connection. Attempted contact via the dedicated Dispatch radio in ZZZ. That was also unsuccessful. Finally contacted Dispatch via VHF phone patch. After conferring with them; a joint decision was made to land at ZZZ. Which would be an overweight landing by ~6000 lbs.The Captain performed all relevant QRH and normal checklists while FO flew. Once ready to return we [requested priority handling] with ATC for overweight landing; with no additional assistance or priority required. Changed control to CA as PF. A normal arrival; approach and smooth landing was performed using maximum reverse thrust and minimal wheel braking. After shutdown all required maintenance log entries and required reports to Dispatch were complied with. Flying an aircraft with half of a dual-redundant system out leaves us exposed to the second system failing too. Once that has happened the rest of the evolution is pretty inevitable. Not that this is a crisis; merely a statistical certainty given large numbers of flights with items on MEL. The largest challenge of the whole evolution was contacting Dispatch for a consultation. Years ago that was simply deemed 'too hard' in most situations and Captains could and did make their decisions mostly unilaterally. In the current era that's not as acceptable as it once was. Given that attitude; it seems important that the system on the airplane actually be reliable for crew use. Which indicates that the on-board router system should be configured to throttle or disable passenger data traffic as needed to ensure the crew voice traffic has priority when needed.