Andreas,
as far as I see, FME's modMCMC should be suitable for your purpose,
examples are given in the the package vignettes:
1. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using
Package FME (same as J. Stat. Softw. 2010 33(3))
2. Sensitivity, Calibration, Identifiability, Monte Carlo Analysis of a
Dynamic Simulation Model
The examples therein can serve as a starting point, just try it out. If
this is not enough, a wide variety of other packages for Bayesian model
fitting can be found in the "Bayesian" CRAN task view.
Thomas P.