I think it's fairly easy, though not a certainty, in '64 if Nixon wins in '60.
JFK could try for a rematch a la Stevenson and Eisenhower, and if it's really close in '60 he's young enough to do it, but would his playboy image casue some problems? Or, would LBJ even use that image to smear him and get his way? There is also Kennedy's Addison's Disease, though i see that as more of a problem by 1968. (Then again, it also means he'd try harder in '64 seeing it as his last shot.)
LBJ was more liberal than many Democrats wanted, but if Nixon is really popular, you could see a number of Democrats backing out like OTL's 1992, and letting Johnson carry the mantle to a likely defeat while preparing for 1968. Combine that with Johnson's own dogged determination to succeed, and I think he could pull enough strings with his alliance in the Senate to get the nomination.
He'll have detractors, and the Kennedy factor, so that's why i say it's not a given, but I think there's a pretty decent chance that Johnson gets the nomination and opposes an incumbent Nixon in '64.