This paper deals with the cooperative source localization problem for a cluster of mobile agents. The goal of each agent is to estimate the relative coordinate of a stationary source in its local frame via a cooperative manner. It is assumed that each agent may or may not have direct range measurements about the source or some neighbors. Collaboration among agents is desired so that every agent is able to estimate the relative coordinate of the source in real time though some agents may not have direct range measurements about the source. A novel discrete-time estimator and a consensus-like fusion scheme are developed for the problem. It is shown that the estimator together with the fusion scheme are globally asymptotically stable under very mild conditions. Numerical simulations are presented to illustrate the effectiveness of the proposed algorithms.