I am estimating differential expression in a time series experiment and some individuals are siblings. I was wonder if there is a specific way to incorporate relatedness into the design matrix for edgeR (or another tool for estimating differential expression)? 

Something like relatedness is probably a bit ephemeral for something like gene expression (this isn't genomics, after all), so you probably don't need to worry about such things. However, you could run your data through voom and then duplicateCorrelation to see what level of correlation you have within the sibs. I would imagine it will be really small, in which case you can probably safely ignore.