The main thing that gives eggs, rotten or otherwise the smell/stench is hydrogen sulfide (H2S), a volatile toxic gas. It reacts with many metal cations (e.g. Copper, Cu +2) to produce a black solid precipitate. I've used it in schemes to separate/identify mixtures of metals which have been digested (oxidized) with nitric acid to produce soluble cations.
I'm not sure if H2S is the best way to blacken copper/brass. I've seen several "recipies" which employ ammoinium carbonate and copper sulfate: Henley's Formulas for Home and Workshop (G. D. Hiscox Ed.: Anvel Books: New York, 1979) gives several "recipies" that are decribed as a "finish" rather than just a discoloration for brass/copper. The most "PC" of these is a referenece to using conc. ammonia with the ore Malichite.
I can give more details if you're intersted?