In recent years, narrative visualization has gained a lot of attention. Researchers have proposed different design spaces for various narrative visualization types and scenarios to facilitate the creation process. As users' needs grow and automation technologies advance, more and more tools have been designed and developed. In this paper, we surveyed 122 papers and tools to study how automation can progressively engage in the visualization design and narrative process. By investigating the narrative strengths and the drawing efforts of various visualizations, we created a two-dimensional coordinate to map different visualization types. Our resulting taxonomy is organized by the seven types of narrative visualization on the +x-axis of the coordinate and the four automation levels (i.e., design space, authoring tool, AI-supported tool, and AI-generator tool) we identified from the collected work. The taxonomy aims to provide an overview of current research and development in the automation involvement of narrative visualization tools. We discuss key research problems in each category and suggest new opportunities to encourage further research in the related domain.