Your challenge, with a POD no earlier than January 1, 1961, is to maintain the Republic of Vietnam as an independent state (even if only nominally so) up to at least 2000. It can re-integrate with the North by diplomatic means any time after that, but should not lose independence by means of military defeat.
The most important questions, to my mind;
1. Can the assassination/removal of President Ngo Dinh Diem either be avoided, given that he was killed in 1963, or be executed deposed more "neatly" as to avoid much of the chaos that ensued IOTL?
2. If Diem is still assassinated, who would be the best choice in successor to lead the nation? I understand that historically, part of what led to the ROV's downfall was a rapid succession of military coups that followed Diem's death. If Diem must still die, how can that disorganization be avoided and a stronger, more cohesive and functional government formed?
3. If Diem is saved for the purpose of maintaining stability, how can his rule be best reformed as to ensure popular support of the government? From what I've learned, he was unpopular and out of touch with the South Vietnamese people at large, in no small part due to his Catholicism and disrespect of the Buddhist population, as well as his and his brother's corruption and their ruthless attitude towards the civilian population in the name of security. How can he, and perhaps more importantly his brother, be reined in while still keeping them content enough to maintain a relative balance of power?
4. How can the insurgency, arguably the biggest military issue facing the South, be defeated or at least minimized and contained?