B737 First Officer reported a generator drive malfunction during cruise. The crew continued to the destination; which was the nearest suitable airport; and landed.

Narrative

At cruise altitude near the ZZZ VOR; the #2 Drive light illuminated. The QRH Checklist was completed; which directed us to disconnect the drive then start the APU. The APU was started; and the generator connected to the #2 side. After about 10-15 minutes; the APU failed; leaving us with one electrical generator. We reran the checklist for the Drive light without an operable APU. This directed us to land at the nearest suitable airport. The Crew; including a Company FO in the jumpseat; discussed and all agreed that ZZZ was the nearest suitable airport as we were only 140 miles out. We [requested priority handling] for a direct flight path to ZZZ. After this; we ran the APU fault QRH. The Captain briefed the Flight Attendants and we all agreed there was no need to brief the Passengers. We decided that would create unnecessary stress on the Passengers. The Captain informed Dispatch of the situation as well. We continued to ZZZ which was VFR at the time. We landed without any further issues. The airport did dispatch the emergency vehicles. We did not request this and did not need any further assistance from them. This was an aircraft malfunction and was handled per standards and procedures. I don't believe there is much else that can be done to prevent this from occurring again. It happens and I believe we are trained properly to handle these situations.