Find out the book, publisher, market, print run, etc,. If its really a non-profit and in the educational market, the fee could be as low as $10-$15 for an inside small image. If thats the case, I personally would probably just ask for a few copies of the book so I can donate them to my local schools and library and give them permission to use it. If its a large print run, and the fees would be higher, I'd ask them for the going rate less a discount (maybe 10-20%) and if they passed I wouldn't loose any sleep over it.
The non-profit card is used all the time. The only time I consider reduced rates or volunteer work is if everyone else in the organization is also volunteering their time, I agree with its cause, and have the time to help out.
If its a traditional non-profit, where everyone is on a salary, and the corporation financially structures itself such they they show no profit, I'll do the same in return. That means I'll keep my salary, but drop the profit from my fees. Thats about a 15%-25% discount, but far from giving away images or working for fee.
If the corporation is 'only' giving up their profits, and the employees aren't giving up their salaries, why should they expect anything more from us?