div background color in print page doesn't work

I would look into the media query way of targeting a stylesheet to the print. I don't believe you will find a common way cross-browser of doing what you want to do (control whether the user's printer prints a background) without using PDFs of your content, which may not be desirable/doable. However, you should consider specially handling your print styles and perhaps avoid backgrounds in your design of the printed page.

http://www.w3.org/TR/css3-mediaqueries/

EDIT

Seeing your other comment, if you have to make the backgrounds print and have a single user, teach your user to make the printer print backgrounds. See for example in Firefox (checkbox):

CSS: box-shadow: inset 0 0 0 1000px gold;

Works for all browsers and on table cells and rows.

Background colors and images don't print by default.

It is a printer option your users could change, but you absolutely can't count on your users knowing or doing that. You cannot control this from the web side (as far as I know).