What was found
(KDAL TO KAPA) AND THE FO WAS THE PILOT FLYING. THERE WERE NO PASSENGERS ONBOARD. AT CRUISE ALTITUDE (FL400) A R GEN LIGHT ILLUMINATED AND WE ACCOMPLISHED THE CHECKLIST. THE GENERATOR DID NOT RESET AND WE TURNED THE GENERATOR OFF. WE ALSO FELT A SLIGHT VIBRATION AT THIS TIME. FIVE TO TEN MINUTES LATER, WE GOT A R ENG VIB LIGHT FOLLOWED SHORTLY AFTER BY A R OIL PRESS LIGHT. THE OIL PRESSURE WAS AT 5 PSI AND THE CHECKLIST LED US TO SHUT THE ENGINE DOWN. WE DECLARED AN EMERGENCY AND ASKED FOR EMERGENCY EQUIPMENT TO STAND BY. ON FINAL, THE CONTROLLER ASKED IF WE WOULD CLEAR THE RUNWAY AND WE SAID WE PLANNED TO DO THAT. WE LANDED AT KAPA ON RUNWAY 17L AND ROLLED TO TAXIWAY A16, CLEARED THE RUNWAY, AND TAXIED IN. WE TOLD THE CONTROLLER WE WOULD NOT NEED FURTHER ASSISTANCE AND, FOLLOWING SHUTDOWN, NOTICED OIL ON THE RIGHT SIDE OF THE AIRCRAFT BEHIND THE RIGHT ENGINE.