As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The underlying model is replaced by a diffusion approximation where a noise term represents intrinsic stochastic behavior and the model is identified using discrete-time (and often incomplete) data that is subject to measurement error. Sequential MCMC methods are then used to sample the model parameters on-line in several data-poor contexts. The methodology is illustrated by applying it to the estimation of parameters in a simple prokaryotic auto-regulatory gene network.