Light Yagami manipulates media coverage to support Kira's actions by strategically leaking information to the media that portrays Kira as a righteous vigilante, targeting criminals and bringing about a safer society. He plants stories that highlight the positive impact of Kira's actions while downplaying any negative consequences or ethical concerns. Additionally, Light uses his intelligence and manipulation skills to influence journalists and sway public opinion in favor of Kira's vigilantism.