The phrase "are at loggerheads" describes a state of disagreement or conflict between two or more parties. Some antonyms for this phrase could include "are in agreement," "have reached a compromise," "are on the same page," or "are in harmony." These words all convey a sense of unity and cooperation rather than tension and opposition. Another possible antonym might be "are indifferent," which suggests that the parties in question do not have strong feelings one way or the other and are therefore unlikely to engage in conflict or disagreement. Ultimately, the choice of antonym will depend on the specific context and the tone that the writer is trying to convey.