White hat methods: Pay for a commercial via TV or radio to convince people to search for your brand+positive keyword.

Ask all of your family, friends or colleagues to search for "your brand+positive keyword".

Co-operate with bloggers and online partners to search for "your brand+positive keyword".

Start a social campaign (FB contest or PPC) to convince people to search for "your brand+positive keyword".

black hat methods - sadly some people take advantage of black hat methods on this one, such as paying for AOL's Mechanical Turks system.