Businessman Donald Trump (R-NY) / Senator Richard Lugar (R-IN)
Senator Joe Biden (D-DE) / Governor James Blanchard (D-MI) ✓
The nomination of Trump is seen as a repudiation of incumbent Republicans while Biden is a better segue out of the New Dealer era than Dukakis. It's still close enough because the GOP had institutional strength at the time but Biden pulls it off. I don't know how well Trump, who I assume would be running more as a libertarian than a populist in 1988, would appeal to the religious right. If he made it through the primaries against a popular sitting vice president, then clearly there's some kind of powerful movement behind him.
This all hinges on Biden campaigning as tough on crime, which was the wedge issue of the day. I assume he would.