To provide coordinate information for the use of intelligent transportation systems (ITSs) and autonomous vehicles (AVs), the global positioning system (GPS) is commonly used in vehicle localization as a cheap and easily accessible solution for global positioning. However, several factors contribute to GPS errors, decreasing the safety and precision of AV and ITS applications, respectively. Extensive research has been conducted to address this problem. More specifically, several optimization-based cooperative vehicle localization algorithms have been developed to improve the localization results by exchanging information with neighboring vehicles to acquire additional information. Nevertheless, existing optimization-based algorithms still suffer from an unacceptable performance and poor scalability. In this study, we investigated the development of deep learning (DL) based cooperative vehicle localization algorithms to provide GPS refinement solutions with low complexity, high performance, and flexibility. Specifically, we propose three DL models to address the problem of interest by emphasizing the temporal and spatial correlations of the extra given information. The simulation results confirm that the developed algorithms outperform existing optimization-based algorithms in terms of refined error statistics. Moreover, a comparison of the three proposed algorithms also demonstrates that the proposed graph convolution network-based cooperative vehicle localization algorithm can effectively utilize temporal and spatial correlations in the extra information, leading to a better performance and lower training overhead.