Motivated by population-based geocoded data for Iowa stillbirths and live births delivered during 2005-2011, we sought to identify spatio-temporal variation of stillbirth risk. Our high-quality data consisting of point locations of these delivery events allows use of a Bayesian Poisson point process approach to evaluate the spatial pattern of events. With this large epidemiologic dataset, we implemented the integrated nested Laplace approximation (INLA) to fit the conditional formulation of the point process via a Bayesian hierarchical model and empirically showed that INLA, compared to Markov chain Monte Carlo (MCMC) sampling, is an attractive approach. Furthermore, we modeled the temporal variability in stillbirth to better understand how stillbirths are geographically linked over the seven-year study period and demonstrate the similarity between the conditional formulation of the spatio-temporal model and a log Gaussian Cox process governed by discrete space-time random fields. After controlling for important features of the data, the Bayesian temporal relative risk maps identified areas of increasing and decreasing stillbirth risk over the birth period, which may warrant further public health investigation in the regions identified.