The way we travel is changing rapidly and Cooperative Intelligent Transportation Systems (C-ITSs) are at the forefront of this evolution. However, the adoption of C-ITSs introduces new risks and challenges, making cybersecurity a top priority for ensuring safety and reliability. Building on this premise, this paper introduces an envisaged Cybersecurity Centre of Excellence (CSCE) designed to bolster researching, testing, and evaluating the cybersecurity of C-ITSs. We explore the design, functionality, and challenges of CSCE's testing facilities, outlining the technological, security, and societal requirements. Through a thorough survey and analysis, we assess the effectiveness of these systems in detecting and mitigating potential threats, highlighting their flexibility to adapt to future C-ITSs. Finally, we identify current unresolved challenges in various C-ITS domains, with the aim of motivating further research into the cybersecurity of C-ITSs.