The word "ballyhooing" refers to promoting something in an exaggerative or noisy manner. Its antonyms would be words that indicate the opposite of such behavior. Some suggested antonyms include downplaying, understating, underrating, de-emphasizing, playing down, or deprecating. Each of these words emphasizes the idea of presenting something in a modest and restrained way, without drawing excessive attention to it. These words also suggest that the focus is on the intrinsic value of the thing being promoted, rather than on hype or sensationalism. Employing these antonyms can help create a more nuanced and authentic promotional message that resonates with your audience.