To open, perhaps it's better to look at the causes of the situation we are in. As indicated in the question, this is not something which is just affecting the NBA; rather it is affecting sports in general. Over the past decade, when the economic health of the West was good, the focus was on winning, and winning as soon as possible. You only need to look at European football for evidence of this. In the English Premier League, just Arsene Wenger (13), David Moyes (7), Rafael Benitez (5) and Sir Alex Ferguson (23) have managed their current sides for 5 years or more. Interestingly enough, these are four of the top teams in England, and none of these four have been the subject of oil-tycoon type takeovers which have resulted in huge sums of money spent on players followed by an interfering owner. Perhaps the best example of a quick trigger finger by an owner in all of sports is Roman Abramovich of Chelsea. To give a bit of backstory, he is a Russian Oil Tycoon who benefited hugely from the breakup of the Soviet Union and the subsequent sale of its oilfields. He took over Chelsea FC in June 2003, and since then they have had 6 different managers (plus a caretaker boss who managed the side for one game). Over this period they have been successful, but any slip ups have been punished with the loss of a job for the top man. It is believed by many that it an interfering culture within the team has also disillusioned the managers resulting in unhappiness, a lack of trust and ultimately poor motivation across the entire team. So how does this relate to basketball? Well, this represents a growing trend of owners paying huge sums of money for teams and demanding immediate success. A quick look at history, however, shows that true success requires a well-built structure that takes years to compile properly.
If this meddling culture does indeed exist within the NBA then it might be tricky for coaches to stay with teams for long enough to truly make their impact. After all, one Championship is generally not going to be enough to send you to the Hall of Fame. Of the coaches currently active in the League, just 7 have spent five years or more at their current teams (and 4 of them have spent exactly 5 years). The average length of time spent at the current team for NBA Coaches is just 3.2 years (interestingly that figure drops to just 2 in the East). For all active coaches (as categorised by basketball-reference.com) the average experience is 7.7 years. Compare this to the average of 20.3 years experience for HoF coaches and you see that there is a huge gulf to bridge. It appears that this would be down to owners demanding immediate success from their coaches and firing coaches before they get the chance to really embed their style on the team. Thus it would appear that it will not only take a special coach and special set of players, but a special owner as well for the next HoF coach.
So where might we find this? We need a good team with a core that will last a few years at least, a patient owner and a good "new breed" coach. To do this I will set a few parameters. To be classed as a coach of the new breed, I will arbitrarily determine that they must have 10 years of fewer of experience. I'm looking for a team with a core that is capable of competing for a Championship for the next 5+ years (or will have competed for 5+ years when taking the past into account).
The first situation that springs to mind is that in Portland. Nate McMillan has proven himself to be a good coach across his 9 years in the NBA. His W-L record is 360-363, so he is as close as possible to being a winning coach. When you consider that his first year with the Blazers was a turbulent one at best (with players like Darius Miles and Zach Randolph getting into trouble on and off the court), that 21-61 record really doesn't seem as though it was down to him. The Blazers have improved steadily at a rate of about 10 games per year across his reign, and it looks as though he has a fantastic core that can really challenge the Lakers atop the West for a long time to come. They have Brandon Roy locked to a new deal, as well as players such as LaMarcus Aldridge, Batum and Oden who could really form a formidable team. The fact that owner Paul Allen has given Nate time shows that he is patient, and I wouldn't be surprised if we are still talking about Nate as the coach of this time in a decade. If that happens, I have no doubt that they would have won at least two titles, and McMillan could by then be on his way to the Hall of Fame.
Another candidate is Byron Scott. He has 9 years of experience and the 2007-08 season with the Hornets was truly a great one. However, they struggled this past year, coming 4th in the Southwest and were dumped out in the first round of the playoffs. We will see in the next year whether it was this or the previous season that was the anomaly. Scott has in general done a good job as a coach (his record is exactly .500) and his record, like McMillan's, is skewed by his first year with the current team (when they went 18-64). New Orleans has a good core in Chris Paul, David West and Emeka Okafor, but it does seem that their financial position could really punish them in the future. It has even been rumoured that they would be willing to trade Chris Paul if it means they could save money in the long run. If this has any element of truth in it, then New Orleans will not be the place to breed a Hall of Fame coach because, if they are willing to trade competitiveness for money, great seasons will be hard to come by.
Doc Rivers is another candidate. He has 10 years of experience and has an overall winning record of 401-348. Rivers has in my eyes shown himself to be more of a people-person that anything else in his time as a coach. He has need developed a revolutionary style, but he has managed to integrate three superstars into one team without a conflict of egos. True, he was aided by the trio's desire for a win (and to do whatever they needed to in order to win that ring) but it is still an achievement in itself to balance three big egos. He also benefits from the fact that his great success has come in Boston, with the team with one of the greatest histories of them all. However, the greatest challenge facing him is longevity; for his star players are ageing, and we are already wondering if, when Garnett returns, he will ever be the same again. Boston should be able to compete for at least the next 2-3 years, but beyond that it could be difficult unless Ainge pulls off another miracle.
Mike D'Antoni's offensive system sets him apart from the rest of the challengers. He brought the run'n'gun offense to the NBA, with great success in the regular season; four consecutive 50-game winning seasons. However, his lack of success in the Playoffs is a serious blotch on his record. However, time is not over, and with the possibility of a star player coming to New York next year, he might be able to engineer a contending team once again. However, whether or not he will be able to overcome that hurdle and actually become a Champion is unknown. What is for sure, though, is that if LeBron does join the Knicks next year, he will demand a competing team, and will demand it immediately, which could ultimately cost D'Antoni his job.
Unfortunately, this candidate will scream out bias for many of you: Mike Brown. I'll admit that he has his shortcomings (notably his inability to coach/devise a good offense), but he statistics really are fantastic. Across his four seasons as a head coach, his W-L record is 211-117 (.643) and he has managed to get the Cavs to the Finals once. He has a good team at his disposal this season, with LeBron, Shaq and Mo Williams as the leading threats to the opposition. He has also added two good complementary players in Anthony Parker and Jamario Moon, kept Ilgauskas, Varejao and West. Add to that the streaky shooter Daniel Gibson, and the Cavs really do have good depth going into this season and beyond. Furthermore, Brown has addressed his shortcoming, and has adopted the American football strategy of essentially hiring an offensive co-ordinator (last season it was John Kuester, new Head Coach of the Pistons) which worked wonders. Whilst this might diminish his personal achievement somewhat, he is still the Head Coach and the statistics are attributed to him. Also, his defensive coaching (learnt under Greg Popovich) is one of the best in the NBA. He has moulded LeBron James into an elite defender, and the Cavs as a team into one of the top defensive teams in the League. The only problem they face is a lack of quickness at the C spot, which the Orlando Magic can exploit ruthlessly. If he can figure out a way to address that problem, the Cavs could do seriously well this season. And if the Cavs do seriously well this season, then LeBron James is likely to stay. If he stays, the Cavs will most likely win multiple titles over the next decade or so, and if Mike Brown can stay as Head Coach, that could be enough to send him into the Hall of Fame.
My final candidate is perhaps a dark horse. Lawrence Frank is the second-youngest coach in the NBA and sits with a 225-225 record. The Nets are in the middle of a rebuilding process, but have a good young core of Devin Harris, Brook Lopez and newly-acquired Courtney Lee. They are quite possibly either 2 major acquisitions or 3-4 years away from competing, but Frank has shown that he has at least some of the attributes required to take them to where they need to be. As a young coach, he might also have potential to move onto a better team in the future and perhaps compete there. I'm not saying he has even a good shot at the HoF, but if the cards fall his way in New Jersey, he could just get there.
In conclusion I still think that Nate McMillan has the best chance, a chance that I would probably rate as about 50-50, but he's not the only one with a fair chance. I also think that Mike Brown and Mike D'Antoni have a good chance (interestingly this hinges largely on which one of the two will be coaching LeBron James come 2010) if they can win a couple of Championships. The rest, however, have only a small chance and require luck, more than anything else, if they are to make it to the Hall.