The short answer is yes, they do exist, but it's hard to know whether you have an original.
I have a black paint Bullseye. I posted a question on the Zeiss Ikon Collectors Group (
http://groups.yahoo.com/group/ZICG/ ) many years ago right after I bought it (off eBay for a very low price), & the late Charlie Barringer (co-author of the "Zeiss Compendium" w/Marc James Small) wrote that it was difficult to know whether a Bullseye was painted at the factory because it was only done to test the market for black bodies & Zeiss Ikon didn't keep records as they did for later models.
"Bernd Otto contends that the all black Bullseyes were randomly taken
from the production line and refinished primarily as "test beds" to get
reaction from the public on whether or not they should go ahead with a
production run. I imagine (presuming nothing about our friends in
Stuttgart) that had they decided to go with a production run of black
bullseyes, they would have done it right with enamel (or whatever
finish material) on brass, as opposed to black on chrome, which is
guaranteed to show wear very fast."
Mine is indeed clearly a chrome body that was painted black, but that's all I know for sure. My guess is that mine was done aftermarket, since it's looks bit amateurish in parts (though some of that could be the result of extensive wear & tear), but I can live the mysterious possibility that it could be a genuine factory job.
