OK, so I should never post anything at 6:00 AM.
It turns out the Time Series task view, not the Econometrics task view, has more details regarding VAR models (https://cran.r-project.org/web/views/TimeSeries.html). Scroll down to the section on Multivariate Time Series Models.
I have not read every vignette for every VAR package, but I'd be surprised if none contain an example of a two-variable problem.