I haven't been able to find a way to set the value of %LEAGUE_BG_COLOR in the game or any style sheets, however you can remove the reference to it and set it directly in the template file that generates that portion of the HTML page.
The file is called "league_title_bar.tpl", and resides in the OOTP templates folder. You'll probably want to copy the whole templates folder into your league folder and edit that copy of it so it only applies to the league you want it to instead of all leagues. You league folder won't have a template folder in it, but if you put the OOTP templates folder in there, it overrides the OOTP one. I think you have to copy the entire templates folder into your league folder for the custom template to work.
Once you've got a copy of the templates folder in your league folder, open the "league_title_bar.tpl" file. There will be two spots where %LEAGUE_BG_COLOR needs to be replaced. Enter the hex code of the color you want preceded by a pound sign (e.g. #FF0000 for red), and remove the brackets. You can also change the color of the text by replacing %LEAGUE_FG_COLOR with a hex code.
So as an example, change
Code:
background-color:[%LEAGUE_BG_COLOR];">
to
Code:
background-color:#FF0000;">
%LEAGUE_BG_COLOR is the blue background color.
%LEAGUE_FG_COLOR is the white text color.
Finally, if you do this with the game open, you'll have to restart the game or switch over to another league and then back for the change to take effect.