TRACON Controller reported a VFR aircraft which had just been handed off to them experienced a malfunction and diverted to a nearby airport. The aircraft turned and descended into an unidentified aircraft in an adjacent facility and the controller could not coordinate in a timely manner due to an extended landline outage.

Narrative

Aircraft X was an ARSA (Airport Radar Service Area) (non-NAS) handoff from ZZZ approach. ZZZ usually changes communication frequency of aircraft on or near the airspace boundary; but when Aircraft X approached the airspace boundary westbound level at 4;500 ft.; I observed the aircraft descend and turn south into unidentified VFR traffic. This point would have been a good time to reach out to ZZZ approach to ensure Aircraft X had the traffic or any other pertinent information. Our shout line with ZZZ approach is OTS (Out of Service) and has been out for over a month. Additionally; the ring line to dial ZZZ ATC facility is OTS between the two facilities. The way of communication is a speed dial line that was added to the ETVS (Enhanced Terminal Voice Switch) on a separate page rather than the main page of the ETVS. That takes some time to navigate to as well as wait for the dial line to ring out; ZZZ ATC facility to subsequently answer the phone; me then to identify myself and ensure I am talking to the right person at ZZZ ATC facility; and then finally solicit the necessary coordination.In this instance; ZZZ approach notified my they had switched Aircraft X; likely before Aircraft X started to turn south and descend; and he may not have taken the frequency change. I reached out again a few seconds after the phone call ended to give time for Aircraft X to switch frequencies. After Aircraft X checked on frequency he advised he was requesting priority handling for loss of fuel pressure and the he wanted to land ZZZ1. At this point Aircraft X was about 3 miles from ZZZ1 descending out of 1;200 ft. I just verified he had the airport in sight and changed him to advisories; not wanting to give too much information during a critical phase of flight. The supervisor later ensured that Aircraft X was on the ground safely. Had the shout line been in service; coordination could have been accomplished in a much more timely manner; ensuring that Aircraft X received better assistance and service during this event.My recommendation is to promptly return the shout line outages between numerous facilities at ZZZ2 that have been OTS for over a month. We are frequently coordination over a phone line; taking attention off of the operation and delaying pertinent coordination for aircraft safety and the operation of the NAS.