Here are some more possibilities.
Richard Nixon
Nixon wins in 1960, but lacking Kennedy's charisma, does poorly with civil rights and loses to Johnson-Humphrey in 1964. Johnson gets low marks for Vietnam and loses support in 1968. Nixon runs again for a split second term and wins.
GHW Bush
Reagan-Bush are elected as in OTL. Reagan is killed on March 30, 1981. President Bush lacks Reagan's appeal and becomes unpopular through the term. In 1984, the media does not break the story of Gary Hart's infidelity, so a Hart-Glenn ticket wins in 1984. In 1985, the story about Hart's affairs does become public, putting him in disfavor. In 1988, Hart wisely decides not to run again and defers support to Glenn. Bush decides to run again and the campaign successfully attacks Glenn for having a wife who stutters. Bush wins a second non-consecutive term.
Twenty-First Century, Al Gore
Gore wins in 2000 but is perceived as weak after the 9/11 attacks. In 2004, John McCain runs a campaign based on his military credentials and wins. Late in his term, McCain loses favor and given his age, decides not to run in 2008. For Gore to run again, he would have to want the job, which was not the case in OTL. Having been president, perhaps some environmental factor motivates him to run again and win.