Boycott Fox by not watching their programming. "Boycotting" by selling their stock is a misnomer.. when you sell for any reason other than a need to reallocate your capital, and without any economic reason, you're just making Fox's earnings less expensive for other investors. A Fox owner who sold 1 million shares last month will see people "boycotting" the stock, and buy the same 1 million shares back this week for a considerable discount. He owns the same percentage of the company, the company has the same profitability, and he'll have made off with a tidy profit.
It's like "socially responsible mutual funds" as a means of social change. Because all these profits of socially irresponsible companies are still for sale on the market (just with a reduced price), it becomes advantageous to buy these companies. Hence the invention of the "socially IRresponsible mutual fund":
http://www.investopedia.com/articles/mutualfund/03/031903.asp