There are many ways to visualize event sequences as timelines. In a storytelling context where the intent is to convey multiple narrative points, a richer set of timeline designs may be more appropriate than the narrow range that has been used for exploratory data analysis by the research community. Informed by a survey of 263 timelines, we present a design space for storytelling with timelines that balances expressiveness and effectiveness, identifying 14 design choices characterized by three dimensions: representation, scale, and layout. Twenty combinations of these choices are viable timeline designs that can be matched to different narrative points, while smooth animated transitions between narrative points allow for the presentation of a cohesive story, an important aspect of both interactive storytelling and data videos. We further validate this design space by realizing the full set of viable timeline designs and transitions in a proof-of-concept sandbox implementation that we used to produce seven example timeline stories. Ultimately, this work is intended to inform and inspire the design of future tools for storytelling with timelines.