Mobile devices are increasingly being used to store and manage users' personal information, as well as to access popular third-party context-based services. Very often, these applications need to determine common availabilities among a set of user schedules, in order to allow colleagues, business partners and people to meet. The privacy of the scheduling operation is paramount to the success of such applications, as often users do not want to share their personal schedule details with other users or third-parties. In this paper, we propose practical and privacy-preserving solutions for mobile devices to the server-based scheduling problem. Our three novel algorithms take advantage of the homomorphic properties of well-known cryptosystems in order to privately and efficiently compute common user availabilities. We also formally outline the privacy requirements in such scheduling applications and we implement our solutions on real mobile devices. The experimental measurements and analytical results show that the proposed solutions not only satisfy the privacy properties but also fare better, in regard to computation and communication efficiency, compared to other well-known solutions. Finally, we assess the utility and expectations, in terms of privacy and usability, of the proposed solutions by means of a targeted survey and user-study of mobile-phone users.