When reading 19th century dictionaries of cant and the vulgar tongue, The Monosyllable (often in all caps) referred to the 'c' word. To put this in context, the 1811 Dictionary of the Vulgar Tongue does not accept either 'c**t' ("a nasty name for a nasty thing") or 'vagina' (undefined) for use in defining any of the many euphemisms for female genitalia; in fact, every euphemism is defined by means of another euphemism -- 'Tu quoque' is the 'mother of all saints' is 'The Monosyllable' is 'A woman’s commodity'. Other books of the era are just as bad.
This gives us no real understanding of how dirty any of these phrases may have been in relation to each other -- all we know is that you couldn't put anything explicit in writing. However, once you've found a good euphemism, run with it! There are references to not only the Monosyllable, but also the divine monosyllable, the venerable monosyllable, and the bawdy monosyllable. Apparently 'The Monosyllable' wasn't just a phrase used by stuffy professors.
This phrase was probably in use before the 1800s, but I can't find any references to it before 1811. It seems to have died out by the 1900s, probably due to people realizing that you could say 'vagina' without being struck by lightning.