We consider inference for demographic models and parameters based upon post-processing the output of an MCMC method that generates samples of genealogical trees (from the posterior distribution for a specific prior distribution of the genealogy). This approach has the advantage of taking account of the uncertainty in the inference for the tree when making inferences about the demographic model; and can be computationally efficient in terms of re-analysing data under a wide variety of models. We consider a (simulation consistent) estimate of the likelihood for variable population size models, which uses importance sampling, and propose two new approximate likelihoods, one for migration models and one for continuous spatial models.