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I had no idea on this one so I posted the question to twitter, and none other than Ben Bolker (!) (Also, Dave Harris) replied to use VarCorr(mod). VarCorr returns a matrix of random effects, but in nlme it’s tricky because it has the class "VarCorr.lme", which xtable doesn’t recognize. So do this:
tbl = VarCorr(mod)
class(tbl) = "matrix"
xtable(tbl)
If you use VarCorr for an lme4 model it is returned as a list of matrices, so you’ll want to extract the list elements but you don’t have to modify the class.
It’s not as pretty as a stargazer table and you’ll have to include it in addition to your standard table, but it has the info you are looking for, I think.
I note that there are a few other packages that generate pretty tables in R Markdown. I like pander. Andrew MacDonald (@poleasunder) made this handy reference chart:

- Noam
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