Off the top of my head, 1987, 2000, the late season adjustments in 2001, and 2010 stand out to me as other candidates. Respectively, a young coach loses 4 seniors and makes it back to the Sweet 16, loses 4 key players (including Duke's first 3 early NBA entries ever) and finishes regular season #1 and ACC Champs, loses Boozer to injury and completely revamps style, and adjusts to alarmingly unathletic personnel and wins 4th title.
And this one deserves consideration already, I'd say. 2010 and 2015 are good years to compare it to. In 2010, we had a veteran team but only had 3 true guards. In addition to adjusting our style (most notably playing a more conservative style of D), psychologically he refused to tell that team they were great. They were mature and secure enough to take that as a challenge. This year, we're young and a little fragile, and he has really talked them up, praising their effort and showing a patience and tolerance where he has often exhibited a stern force of will. Last year we also had a bunch of freshmen in key roles, but they were OAD good and he hasn't coached this team the same way, despite similar profiles regarding age.
And even just on its own, w/o comparisons that show K's genius for adjustment, he has taken a hobbled team w/ no depth and glaring weaknesses and made it work. Losing 4 out of 5 could have snowballed far worse, but we're now on a 5-game winning streak, including 3 in a row over teams ranked well above us.