Hi, Jagdkommando...
I've checked through the unit codings for ?K as a Geschwader I/D code, but can't find anything that pointed towards an He59 being on strength. This is not to say a ?K coding wasn't used, however. The two most famous units which spring to mind are 5K (KG3) and 9K (KG51). It wouldn't surprise me, but I'm not aware of He59s serving with bomber units...
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So, to my mind, it's more likely that the code would be CK+ZU. Bearing in mind that He59s often undertook air/sea rescue duties, and those units sometimes had fully alphabatic codes, this would be my guess. However, 'C' under the starboard wing might pose a problem, as many aircraft with fully alphabetic codes had them repeated in full under the wings, so your machine would perhaps more likely have had C+K under the port wing and Z+U under the starboard.
Hope this may go some way to helping you. It would be interesting to see the picture, though, if you were able to share it.
Regards...