The first thing that comes to mind is that Johnson might have lived past December 18, 1970. With some rest instead of another term, Johnson could have lived well into his 80s. And that was with him coming up with the October 1968 surprise that drew down the Vietnam War.
In any case, if LBJ could win reelection despite the party being divided, I should think that pretty much any alternative nominee would have likely won as well. Humphrey, RFK or McCarthy would each probably have beaten Nixon.
Other than that, I think you probably have a scenario in the 1970s that plays out pretty much the way OTL did: a Democrat wins in 1972, loses to Reagan in 1976 due to the economy with the Reagan term being disastrous both internationally and economically and some Democrat sweeping into office in 1980.