Both Haig and Dole despised Bush. Quayle was a sop to the right-wing true believers; in the same vein you could have Jack Kemp, Dick Cheney, or Pete du Pont. John McCain was a bit too enmeshed in the Keating 5 scandal at the time, but he was still 12 years younger than Bush, and a war hero; he could have worked. It does depend a bit on who Dukakis picks. If he chooses Glenn, then McCain could work to counter that; if he chooses Martha Layne Collins, Bush could choose Lynn Morley Martin.
Or, alternately, he could go the 'reinforcing' route, unlike choosing such a bizarre contrast as Quayle (who merely reinforced that Bush was old, moderate, and not particularly attractive.) Richard Lugar, Dick Thornburgh, or Arlen Specter could be competent, intelligent, reasonable choices.