The advancement of molecular profiling techniques fuels biomedical research with a deluge of data. To facilitate data sharing, the Global Alliance for Genomics and Health established the Beacon system, a search engine designed to help researchers find datasets of interest. While the current Beacon system only supports genomic data, other types of biomedical data, such as DNA methylation, are also essential for advancing our understanding in the field. In this paper, we propose the first Beacon system for DNA methylation data sharing: MBeacon. As the current genomic Beacon is vulnerable to privacy attacks, such as membership inference, and DNA methylation data is highly sensitive, we take a privacy-by-design approach to construct MBeacon. First, we demonstrate the privacy threat, by proposing a membership inference attack tailored specifically to unprotected methylation Beacons. Our experimental results show that 100 queries are sufficient to achieve a successful attack with AUC (area under the ROC curve) above 0.9. To remedy this situation, we propose a novel differential privacy mechanism, namely SVT^2, which is the core component of MBeacon. Extensive experiments over multiple datasets show that SVT^2 can successfully mitigate membership privacy risks without significantly harming utility. We further implement a fully functional prototype of MBeacon which we make available to the research community.