Several simple ways to do it- for instance, what if Al Gore decides not to run in 2000 (for whatever reason- perhaps a personal health issue)? Biden jumps in early in the primaries, and picks Lieberman to get moderate support against a McCain ticket.
Or 2004 (perhaps without Iraq?) sees Biden jump in and ends up presenting a sort of middle ground between firebrand Dean, establishment Kerry, and warrior Clark, and he includes Lieberman on the ticket to try to pick up moderates and give a strong foreign policy boost to the ticket.
But the Two Old White Guys ticket seems more like a Dole-esque retirement present- perhaps a 2012 run in a world without the economic crash and a popular Republican incumbent- I'm thinking McCain/Graham or something to make the oldest, whitest presidential race possible.