The phrase "staid the course" implies a sense of steadfastness, consistency, and dedication towards a particular goal or path. Its antonyms would be words that signify deviating from the said path, or changing it altogether. Some antonyms for "staid the course" could be "fluctuate," "waver," "veer off," "stray," or "diverge." These words suggest a lack of consistency, deliberation, or focus, which is opposite to the idea of staying the course. While it's important to be flexible and adaptable at times, there are situations where it's crucial to remain steadfast and committed towards a particular objective, and that's where the phrase "staid the course" comes into play.