An incredibly mind-numbingly boring achievement. I mean, what coach has (or will ever!) coach for 60 years??
Set up a new dynasty. You can then choose to play through all 60 seasons (if you're that hardcore), or sim the seasons (or a combination). If you sim, you have to re-sim for the conference championship week, the bowls, the offseason, and the preseason. In other words, you have to tell the game to sim five different times to get through a single year (rather than, say, simply "sim to next season").
The team doesn't matter, but better teams will have more success recruiting, etc., and so you won't have to worry as much about getting fired since the game is simming better recruiting for you. If you start having bad seasons, you can just take over, sim-and-save week-by-week so you have a better record, or actually, you know, play the games.
If you get fired, it isn't a problem since there's some school out there that needs a coach. Just keep plodding through the years. Oh, and grab a couple of movies for your laptop while you press the sim button over and over again.