The continuous evaluation of queries over an event stream provides the foundation for reactive applications in various domains. Yet, knowledge of queries that detect distinguished event patterns that are potential causes of the situation of interest is often not directly available. However, given a database of finite, historic (sub-)streams that have been gathered whenever a situation of interest was observed, one may aim at automatic discovery of the respective queries. Existing algorithms for event query discovery incorporate ad-hoc design choices, though, and it is unclear how their suitability for a database shall be assessed. In this paper, we address this gap with DISCES, an algorithmic framework for event query discovery. DISCES outlines a design space for discovery algorithms, thereby making the design choices explicit. We instantiate the framework to derive four specific algorithms, which all yield correct and complete results, but differ in their runtime sensitivity. We therefore also provide guidance on how to select one of the algorithms for a given database based on a few of its essential properties. Our experiments using simulated and real-world data illustrate that our algorithms are indeed tailored to databases showing certain properties and solve the query discovery problem several orders of magnitude faster than existing approaches.