This is one area of the game that I'd love to see improved down the road.
To have a payroll who's budget depends on a number of factors would be kool.
Attendance, wins/losses, wins at home, wins vs winning ball clubs, winning or losing trends, star players, traditions, stadium, stadium condition, advertising deals, media contract choices, ticket prices and promotions.
Have a few attributes for coaches that relate to public relations. Such as pre-game interviews, post-game interviews, reputation, the kind of offense or defense they like to run, and what kind of temperament they have. Example: A hot headed coach might be much more liked in Philly than they would be in San Francisco. As long as their winning of course. :)
I prolly overlooked some stuff but for me this would be fun. Trying to keep your head above water is half the battle in managing a franchise. Also make the whole coaching deal more in depth and relevant. But that's a whole other topic in itself.