This manuscript explores the viability of using optimal point process (Snyder) filters in order to estimate the underlying parameters of the variable population size coalescent process. Estimating these population parameters is an important area of research in phylodynamics, especially given the widespread use of the coalescent in modelling the relationship between the genetic diversity and epidemiological dynamics of human pathogens. A variety of coalescent estimators based on a diverse set of techniques, such as skyline plots, Bayesian and Markov Monte Carlo approaches, already exist. However, at times these methods are inflexible, or difficult to use and there is a need to explore new estimation techniques. This Snyder filter is proposed here as a new alternative for optimal coalescent inference and parameter estimation. Through its application, first to a canonical set of demographic models and then to empirical data from the Hepatitis C epidemic in Egypt, the filter is shown both useful and capable. The Snyder filter is exact (makes no process approximations) and is optimal in mean square error. Since its implementation is simple and it was originally developed to estimate stochastic parameters, Snyder filtering holds much potential for coalescent estimation.