It would never have occurred to me to make carbonnades with anything but beer or ale but, as I wrote above, all recipes are merely jumping off points for real cooks. Making a good stock is as easily done with game as with domestic meats. I might try a fair bit of wine with the broth, selecting a wine and quantity that will compliment, not overpower, the meat. (I was once served elk chili with a sauce that so overpowered the elk that the meat could have been almost anything. Why waste elk so?) If you try carbonnades without beer or ale and it works for you, let us know.
Gee, I'd love to see your data!