Alternately, you could have Clinton fail to recover from the nadir of his unpopularity in 1994, at least to the extent he did. Now this would essentially require Newt Gingrich not being Newt Gingrich, no government shutdown etc. If the impression that dominated political discussions in early 1995 continues into 1996, that is Clinton's already a lame duck and Gingrich/whoever the leader of the House happens to be, is the one who is really controlling government policy, if the impression of Clinton being incredibly incompetent continues, Dole might have a genuine shot. Given the economy, not a great one, but if Clinton wades through 1995 and 1996 looking less like a President and more like a washed up has-been, we might be looking at President Dole come 1997.
It's worth noting that after the 1994 election Clinton was all but written off as a one term President in the eyes of the pundit-class, by 1996 his reelection was essentially a sure thing. Now to an extent, that's the economy's effect, but there are other reasons why Clinton was able to recover his popularity in 1995, and if you want Dole to have a chance, you probably have to sabotage the other factors to the greatest possible extent.
You need Newt Gingrich not to be Newt Gingrich.
Or you could contrive things so the election goes to the house...