No circa 1800 depictions, outside of scientific works. Even then, many of the drawings clearly show that the artist didn't understand what the heck they were drawing. I'm pretty sure that I have seen just about every drawing or picture of any airgun previous to about 1855 or so. I've certainly have vigorously searched for them.
Most all the other Austrian firearms were depicted in the Ökonomie-Musterbücher, along with all the many various swords, etc. but the airguns themselves are not covered. Interesting to note that the accessories are covered. So, yes, we have great drawings of other Austrian weapons of the same age, no airguns.
There is a drawing of a Girandoni in Haller, 1891, but this is the later English-made model.
Note: the whole story starts to get very complicated beyond this. The book I'm working on is past 400 pages in my attempt at trying to explain it all.