This paper studies the problem of distributing a content service in Cloud of Clouds to satisfy a sequence of mobile request demands with minimum monetary costs. A content may have single or multiple replicas, each being stored in one or more virtual machines (VMs) to facilitate the accesses via downloading to or replicating at (i.e., migrating) the VM sites where the mobile requests are made. As the origins of the mobile access patterns are frequently changed over time, this problem is particularly important for the users to achieve improved QoS for those time-bounded services and also beneficial to the service providers to minimize the expense on using the cloud infrastructure as well. However, these benefits do not come without compromise. The content distribution comes at cost of bulk-data transfer and service disrupts, which may increase the costs of the services. In this paper, to reap the content migration benefits while minimizing the service costs, we propose an online heuristic algorithm based on the local-search techniques to migrate the content replicas in adaptation of the mobile access patterns. For comparison purposes, we also study this problem in its off-line form, and propose a heuristic to evaluate the algorithm via a YouTube trace-based simulation. The simulation results show that our algorithms can effectively adapt to the changes of mobile access patterns to efficiently satisfy the user requests in a cost effective way.