We investigate zero-shot cross-lingual news sentiment detection, aiming to develop robust sentiment classifiers that can be deployed across multiple languages without target-language training data. We introduce novel evaluation datasets in several less-resourced languages, and experiment with a range of approaches including the use of machine translation; in-context learning with large language models; and various intermediate training regimes including a novel task objective, POA, that leverages paragraph-level information. Our results demonstrate significant improvements over the state of the art, with in-context learning generally giving the best performance, but with the novel POA approach giving a competitive alternative with much lower computational overhead. We also show that language similarity is not in itself sufficient for predicting the success of cross-lingual transfer, but that similarity in semantic content and structure can be equally important.