You are using an old version of baySeq - please upgrade. The 'pairedData' class has been obsolete for several release cycles.
Alternatively, you are using an object created with an old version of baySeq in a newer version of baySeq. The easiest way to resolve this is usually to re-run the scripts which created the object. If this is problematic there are alternatives, but these are messy and require hacking about at the slot level of your objects.
Ok - it's the example that is out of date. If you look at section 2 of the vignette at http://bioconductor.org/packages/devel/bioc/vignettes/baySeq/inst/doc/baySeq_generic.pdf you will find the current procedure for paired data analysis, which is to construct a countData object with a three-dimensional data structure; e.g.
pairCD <- new("countData", data = array(c(pairData[,1:4], pairData[,5:8]), dim = c(nrow(pairData), 4, 2)), replicates = c(1,1,2,2), groups = list(NDE = c(1,1,1,1), DE = c(1,1,2,2)), densityFunction = bbDensity)