B-757 First Officer reported a pressurization malfunction during cruise. The crew diverted to an alternate airport and landed safely.

Narrative

Show; brief; taxi; takeoff all uneventful. Background: At cruise altitude; over water; the autopilot disconnected without prompting. This illuminated a red warning on EICAS with associated horn. The Captain was Pilot Flying (PF); and took controls. He was able to rearm autopilot with no issue.Issue and emergency: About 10 minutes later another horn sounded and a warning EICAS displayed Cabin Altitude". Both the other pilot and I looked up to where the pressurization panel is located. We both noticed that the cabin pressure was above 10k feet. The Captain stated "let's get our masks on and run the checklists". We both simultaneously got our masks on and established comms.I ran the cabin altitude QRC; and switched auto controllers as prescribed; from 1 to 2. There was no noticeable change. I tried manual mode; which made little difference. When I came to the emergency descent section; I confirmed with Captain; ran through the checklist and then [requested priority] with ATC. The Captain continued flying and ensured all flight controls correctly set up including using speed brakes.We started descent and began looking again at manual mode pressurization. It seemed to still have very little change. At that point I offered to take controls of jet. Captain agreed. I continued descent to 10;000 ft.During this time the captain worked through remainder of checklist (electronic); and we discussed our option of proceeding to ZZZ; the nearest large airport. I told ATC of our intentions. At this point we were level at 10;000 ft; so the Captain took his mask off and called Flight Attendances (FAs) and informed them of what had happened. He then called Dispatch to confirm the our plan. We set up the approach into ZZZ together; planning on an ILS XX; with good weather conditions. The Captain took controls back and I proceeded through descent checklist and communicated with ATC. The recovery and taxi to gate was uneventful."