Having Nixon win in 1960 is fairly easy (e.g. have him cancel his Alaska trip, thus giving him more time to prepare for the first Presidential debate). 1964 would surely be his year as well.
Your challenge is that after Nixon, the populists Dems win in 1968. There is a restriction: The black vote is firmly with the GOP by that time, with Nixon passing civil rights laws and voting rights laws (it could he watered down, but not to the point where they can't be a voting bloc).
The final result should be a TL in which the New Deal consensus is retained, with the social conservative-economic conservative alliance not occuring ITTL. A TL where the US is still racially liberal, but with a counterculture crushed and sexually conservative (I'm interested with this because there's already an abundance of liberal TLs on this site).
Bonus points if you get JFK to win and lead a mainly populist Democratic Party.
Highest points if you have George Wallace win the Presidency as a Democrat, and water down his racism (e.g. have him visit an MLK that gets wounded during a race riot or a near assassination or something, making him turn back on his radical positions for political gain).
Both JFK or Wallace must serve two terms.