There are many successful NFL and college head coaches that have come off the Bill Parcells coaching tree. I am doing this by memory, so I may miss one or two, but here goes:
Coughlin, Bellichick, Handley, Groh, Crennel, Weis, Erhardt, Fassell (though he was hired by Parcells but never worked under him.... Parcells quit before Fassell started). Let's not forget Tony Sparano and Sean Payton who coached under the Big Tuna in Dallas. I think even current Jets coach Eric Mangini worked for a while under Parcells in New England. That's a fairly impressive list and there are some others who are prominent assistant coaches that I left out, including Mautice Carthon among them.
Parcells was the best special teams coach ever and knew more about catching punts and blocking for the return than any other coach. In his Superbowl year in New England, in addition to being HC, he was also special teams coach. It was somewhat ironic that they lost that Superbowl to the Packers largely on the special teams returns of punt/kick returner Desmond Howard.
One of Parcells great strengths, aside from X-es and O-s was that he is reputed to have been a great motivator of his team. He believed in instilling fear and badgering his players to motivate them and felt that a player afraid of losing his job played with a little edge and played better. I believe Coughlin followed this pattern and fortunately realized last year that times have changed, players are different now and you need to have a better working, respectful and professional relationship with your players. That's why his player's council and slightly easier style worked so well last year.
Despite his severe, riding attitude, one of the things Parcells always did was to not beat a player when he was down and not to build him up when he was on top of the world. He believed in team first, in keeping everything on an even keel. So when the Giants used to go on a short losing streak, instead of yelling at them and railing at them through the media, he would be conciliatory, supportive and kind in trying to rebuild their confidence. When they won a few games in a row and looked good, that's when he would come down on them and find flaws in every play that didn't work, to make them apply themselves and work harder.
I can't help but think that Coughlin learned this little lesson from Parcells and we saw a little example of it this week. Giants were on top of the world and breezing through the league at 11-1, but Coughlin was very workmanlike and somewhat muted in his praise. He kept talking about things that the team has to correct and work on to play better. Then the Giants hit a little skid and lost these last two games. So what does Coughlin do - come down hard on his players, chastise them for playing badly and try to browbeat them into playing better? No - that would have been the exact wrong thing to do. Players were trying hard, the effort was there. By coming down hard on his players, Coughlin would have only increased the pressure on them and - if they were playing tight - would have made them feel the pressure and start playing even tighter. Instead, Coughlin did precisley what he should have done and what he did this week. He got up before the media all smiles and joyful excitement. he did some jumping jacks, for gosh sake, to show how pleased he was with the team's position. He took the big picture approach and reminded everyone that the Giants are exactly where they wanted to be at this point of the year: with the division and a playoff berth clinched and in great position to get a bye and home field advantage for the playoffs.
There's no doubt that Coughlin is a superior X-es and O-s coach, prepares fastidiously and is a great special teams and offensive coach. These skills he developed on his own and gleaned from the master Parcells. It seems to me that he also inherited the philosophy of motivation from the Big Tuna: deflate them a little when you see they're getting overconfident, but pump them up when they need it, and that may be even more important.