We present a Bayesian method for the reconstruction of pedigrees in clonal populations using co-dominant genomic markers such as microsatellites and single nucleotide polymorphisms (SNPs). The accuracy of the algorithm is demonstrated for simulated data. We show that the joint estimation of parameters of interest such as the rate of self-fertilization is possible with high accuracy even with marker panels of moderate power. Classical methods can only assign a very limited number of statistically significant parentages in this case and would therefore fail. Statistical confidence is estimated by Markov Chain Monte Carlo (MCMC) sampling. The method is implemented in a fast and easy to use open source software that scales to large datasets with many thousand individuals.