Early diagnosis and localization of myocardial ischemia (MS) and coronary artery stenosis (CAS) play a crucial role in the effective prevention and management of ischemic heart disease (IHD). Magnetocardiography (MCG) has emerged as a promising approach for non-invasive, non-contact, and high-sensitivity assessment of cardiac dysfunction. This study presents a multi-center, AI-enabled diagnosis and localization of myocardial ischemia and coronary artery stenosis from MCG data. To this end, we collected a large-scale dataset consisting of 2,158 MCG recordings from eight clinical centers. We then proposed a multiscale vision transformer-based network for extracting spatio-temporal information from multichannel MCG recordings. Anatomical prior knowledge of the coronary artery and the irrigated left ventricular regions was incorporated by a carefully designed graph convolutional network (GCN)-based feature fusion module. The proposed approach achieved an accuracy of 84.7%, a sensitivity of 83.8%, and a specificity of 85.6% in diagnosing IHD, an average accuracy of 78.4% in localization of five MS regions, and an average accuracy of 65.3% in localization of stenosis in three coronary arteries. Subsequent validation on an independent validation dataset consisting of 268 MCG recordings collected from four clinical centers demonstrated an accuracy of 82.3%, a sensitivity of 83.8%, and a specificity of 81.3% in diagnosing IHD, an average accuracy of 77.3% in localization of five myocardial ischemic regions, and an average accuracy of 65.6% in localization of stenosis in three coronary arteries. The proposed approach can be used as a fast and accurate diagnosis tool, boosting the integration of MCG examination into clinical routine.