The southeastern conference
The Big Ten has won 39 National Championships in College Football. Far more than any conference. I will qualify this answer and one of my other answers by saying that I am only including Championships at the highest level. For Example, the Ivy League has won more than 39, but many came as an FCS competitor. Technically, Division III Ohio Valley Conference has won by far the most, but I am keeping my answers (which actually are accurate) to Championships won at the highest level.
SEC
Judy Devlin won 8 consecutive national titles starting in 1955 and ending in 1963.
The Green Bay Packers have won three National Football Conference championships since the National Football League's merger with the American Football League in 1970. Green Bay won the titles in 1996, 1997 and 2010.
Miami
None.
Alabama
I assume you mean SEC, 4 consecutive
4 National Titles. I
2
Princton
One in 1939
Alabama