This is pretty tough, There wasn't a whole lot of appetite among '80s Democrats for moderates as presidential candidates. 1980 is all but impossible; the challenge to Carter was from the left, not the right. Ditto with Mondale in 1984.
I suppose one way to go would be a Carter death pre-1980, with President Mondale losing badly to Bush as a GOP nominee, causing the party to shift right a bit. Bentsen runs in 1984, wins the nomination and picks Dukakis as VP (in this scenario, Dukakis avoided the 1978 primary loss to Ed King and was re-elected in both 1978 and 1982). Your pick whether Bush or Bentsen wins.
One scenario does clearly work: Dukakis dies for some reason soon after the 1988 convention and the DNC picks him to replace him at the top of the ticket and the two face off in the fall of 1988. However, the POD there is later than you specified.