Causal discovery from observational data has been intensely studied across fields of study. In this paper, we consider data involving irregular occurrences of various types of events over the timeline. We propose a suite of scores and related algorithms for estimating the cause-effect association between pairs of events from such large event datasets. In particular, we introduce a general framework and the use of conditional intensity rates to characterize pairwise associations between events. Discovering such potential causal relationships is critical in several domains, including health, politics and financial analysis. We conduct an experimental investigation with synthetic data and two real-world event datasets, where we evaluate and compare our proposed scores using assessments from human raters as ground truth. For a political event dataset involving interaction between actors, we show how performance could be enhanced by enforcing additional knowledge pertaining to actor identities.