I don't know if you necessarily have to kill Nixon to achieve a Rocky presidency. How about a slightly different POD?
1956: Eisenhower drops Nixon from the ticket in favor of Massachusetts Governor Christian Herter. Nixon takes over at Defense, and the Eisenhower-Herter ticket destroys the Stevenson-Kefauver ticket in a fashion similar to OTL's. Fast forward to 1959, when Governor Rockefeller formally decides to enter the race for the Republican nomination. Senator Goldwater also signs on, as does Defense Secretary Nixon.
Nixon, with a bit of a stigma about him for having been dropped from the ticket and a lack of strong public attention for the past four years, probably doesn't do as well as he did IOTL, wherein he'd put himself in an especially strong position to run for the Presidency, come 1960. With this in mind, the Eastern Establishment types rally around Rockefeller, who comes out on top at the convention.
Rocky beats Kennedy by a small margin, picking up a few states in the Northeast that Nixon was unable to carry IOTL. Rocky's administration is probably similar to OTL's Kennedy administration, though I think that Rocky probably has a better time dealing with the Congress than Kennedy might have (Senators-turned-Presidents generally have a terrible time at working with Congress, unlike Governors-turned-Presidents). He probably maintains good enough relations to get Civil Rights and some welfare measures through, but by the time '64 rolls around, he might be headed for some trouble himself. I expect that an earlier push for Civil Rights in 61-63 might produce the same effects that went on in 66-68 to happen around 64-65 instead, with open rioting in the streets. This, combined with Democratic demagouging on Rocky's nonexistant aid to South Vietnam, probably puts a nice dent into his poll numbers.
By 1965, Rocky is out of office, and the Democrats are back in power after twelve years in the wilderness. President Henry M. Jackson promises 'law and order' at home, to protect the Civil Rights of African-Americans, confront communism abroad, and to enact a universal health insurance program. The next eight years see Civil Rights protected with the additions of the 24th and 27th Amendments (OTL's former and an ERA for the latter), a wider scope for environmental protection on the part of the government, Medicare and Medicaid, and American troops setting foot on Vietnamese soil for the first time.
Jackson's ascension to the leadership of the Democratic Party probably does enough to help mend relationships within the New Deal coalition. His social legislation keeps liberals and the unions on board, his opposition to busing keeps large areas of the south on board, and yet, his support for Civil Rights and Affirmative Action keeps blacks on board, as well.
Rocky's loss, on the other hand, does a bit of hand wringing within the Republican Party. Some milder conservatives join with the Rockefeller camp to form a coalition of social moderates and social liberals, but economic conservatives. The more extreme, reactionary elements bolt the party to merge with the new 'American Party' led by George Wallace, and do well in the South and midwest for a time.