My choice:
Please note that it is killing me to type this information out, as I do live and die with my beloved Terps (Go Maryland!) and really like Gary Williams as a coach. He's one of the best in the business, and I'm really, really happy he's at Maryland. There are few others that I would take over him as a coach, and the information below will give that information away.
I look at an argument like this one -- picking the best coach for winning a championship -- and surmize that I need to pick the person that gets the best from his players, and puts his players into a position to win. Such a coach has to be willing to adjust his system to his players, and should be able to win championships with many different versions of a team. It's easy to look at some teams and see that they have been put into position to compete because they have star players. Players that can almost single-handedly, or in some cases absolutely single-handedly win. Coaches that are lucky enough to get such players can have a long career if they wish simply enjoying the ride. Some might point to Phil Jackson in both of his championship runs (with the Bulls, and later with the Lakers) in the NBA and easily identify such a coach.
There's been a few coaches in the history of the NCAA (while I've been following) that have enjoyed similar gifts from the basketball gods. The coach of the Fab 5 as an example, where the players clearly made the team, and the coach wasn't so much responsible for the wins as the players were.
Even my favored local coach, Gary Williams, has done a little of this, riding the hard work of one of the most dedicated ball-players ever, Juan Dixon, to a championship.
So, as I sit and think of great coaches that I have seen, and what a difference I thought those coaches have made to their teams, I come up with a fairly short list.
My own choice, as much as it pains me to type it out, would be Coach K. He of the hated ACC rival, Duke Blue Devils.
I remember a few seasons back when Coach K had back problems and was away from the game for an entire season. At that point in time, Maryland was struggling. They (the Terps) finally, without Coach K there, were able to start to win a little against the hated Dukies. That season taught me just how valuable Coach K was to that team. You see, without him the Dukies were just fodder along the way. The following season, with virtually the same team, Coach K came back and took his team well into the post season. A swing of double digits in the win column (or so it seemed).
For that reason, I can point to Coach K and defend him easily as the coach I would take if I had a team on the cusp of winning.
I might be able to point to a Bobby Knight or even a Dean Smith as also rans for the position, but to me those coaches are not quite at the same level as Coach K. He wins no matter who is on the court, and his teams consistently perform up to and above their expectations.
As much as I hate him when he is coaching against the Terps, he's the one guy I would turn to if I really wanted to win.
So, to Coach K, at least from my side - /salute