AchimW,
Cochenille is also used to dye yarn for weaving. It is the source of the red yarn in Navajo rugs produced before about 1900. It has been largely replaced by commercial dyes, but it is still used by weavers to color hand-spun yarn for special projects and restorations.
My wife is a weaver with an interest in Navajo rugs. She has attended dying workshops where cochenille was discussed and used. A couple of other natural dyes that might be useful are indigo (blue) and onion skin (yellow to brown). Both are cheaper and more available than cochenille.
The source of supply would be weaving/spinning shops (although we haven't seen any locally. I don't know if retail weaving shops are common in Germany, but there should be sources of supply available on the web. Do a search using 'dye', 'yarn', or 'cochenille'.
A couple of cautions are in order. First, the dying process for yarn involves boiling the yarn in the solution. I don't know how the antler will react to this. The second and more important caution is that the bright, intense colors are obtained by adding "mordants" to the solution. They are generally heavy metals (chromium, etc.) or metal salts. THE FUMES CAN BE EXTREMELY TOXIC. Do this outside (with a lot of wind blowing if possible). DON'T LET THE SOLUTIONS COME INTO CONTACT WITH THE SKIN IF POSSIBLE. Use rubber gloves and tongs to handle the material being dyed. I don't mean to discourage you, but the people we know who do this regularly (some for a living) are uniform in their caution (like knife makers).
I hope this helps. Good luck. Please post the results if you do go ahead with the dying project.
Thanks,
Bob Couture
P.S.
It also occured to me that a good quality commercial dye intended for use on wool (animal fiber) might also work pretty well and be a lot less trouble.