In that case its easy as pie.
1966 or early 1967 (i.e. before public opinion swings against the war)
Fortify the DMZ, pending a free and final vote on a new Vietnamese government. Make use of the UNSC veto as needed.
Settle in for a fairly brutal three-five years of bug hunting. Spend some money on a "mini-Marshall Plan" across the entire country. Get some light industry/manufacturing/investment (both from the U.S. and from the IMF) and reduce the amount of grinding poverty. This might turn around and bite at some point, since the U.S. is effectively setting up another Asian Tiger, but people who have money, food, and shelter tend to be less likely to go hide in the jungle as VC.
Easy?
South Vietnamese (and Americans) were not outfought as much as out-administered. Unless GVN/USA is able to destroy FNL political and administrative structure and replace it with their own then invasion of the North would result in never ending guerrilla war ála First Indochina War. China and USSR still have every incentive to provide NVA/FNL with safe areas, supplies and training.
If there is an effective popular government in Saigon, then there is no need to invade north, if there is not then it doesn't help. Best bet? Have USA join the French in 1955 and support a coalition government with Buddhist, Hoa Hao, Cao Dai and Bình Xuyên. Abolish tenant farming with land reform, develop infrastucture and industry. Basically hijack Viet Minh political program minus the communism and maybe, just maybe South Vietnam can go along with the Malaysia, Korea and Thailand