B767 Flight Crew experiences generator failure enroute to Europe and cannot be reset. APU is started and assumes its share of the electrical load but not for long. APU starts and fails several more times during diversion to suitable airport.

Narrative

Enroute to ZZZZ; engine Generator Off (Right) EICAS displayed with warning lights. Right Generator Off checklist performed while starting the APU; with no reset. APU picked up the load. I was handling ATC and flying; while the Captain was in a SATCOM conference call. It was determined after another generator reset that failed; that it was OK to continue to ZZZZ with the 2 operating generators. At around 68 miles west; an APU fault was displayed on EICAS and followed by an immediate automatic shutdown of the APU. We declared an emergency and started heading toward ZZZZ1. Relief Pilot returned back to the cockpit to assist with the situation. After coordinating with Dispatch and running the APU Fault checklist; it was decided to head back to ZZZ when the APU generator was brought back on line. APU was restarted 2 more times; even after descending to FL260 to help the APU out. An emergency was re-declared and a determination to continue to ZZZ was reached based on our current position. A final attempt to restart the APU was done on final; but it shut down shortly after. A heavy weight landing was performed by the Captain. Taxied to the gate and released the brakes after the chocks were in place. Supplemental information from ACN 832899: I returned to the flight deck to find us in a descent to FL320. Right generator off line; APU Fault message and APU shutdown and checklists all complete. The Captain was just confirming with Dispatch our new destination. Briefed emergency status and confirmed decision to divert. Executed a successful restart of APU which accepted the electrical load. Informed Center Controller of downgrade to non-emergency status. I reviewed the Divert checklist; and we decided to continue to ZZZ. Despite descending to FL260 to aid the APU; it failed 2 more times with immediate successful restarts. After the last failure; since we were split difference between several divert points; we elected to continue to continue to ZZZ but re-declared emergency. Restarted APU on final but it failed within 2 minutes. Landed without event overweight.