It is not so difficult to find an avenue of heter for permanent makeup, even if one would be hesitant to practically rely on it.
While a tattoo that is not idolatrous in nature is forbidden (at least mid’rabbanan) according to normative halacha, there is a case where it is permitted. The Shulchan Aruch (YD 180:3) notes that it is permitted to place ashes on a wound, even if doing so will essentially tattoo an indelible black mark on one’s skin.
The question is, why?
If the reason is because of the pain of the wound, than this case has little applicability to the permanent makeup case. If the reason is because it is just a splotch without form, also, this case will have little applicability to our makeup question.
However, the poskim do not say these reasons. Instead, the Beis Yosef and the Shach* state clearly their view that the reason is that the presence of the wound makes it obvious that it is not an idolatrous tattoo.
The fact that they opted for this reason without mentioning anything else implies that this is sufficient reasoning to permit a tattoo. That is, even without the wound factor, if a tattoo is inherently discernible as not idolatrous, it should be permitted.
While one may be reluctant to apply this reasoning with regard to a regular tattoo simply because what is discernible in one place may not be discernible in another, with permanent eyeliner one can probably advance the argument that it is clearly and obviously devoid of any hint of idolatry (since it is obviously a substitute for something every woman does for beauty) and it is therefore permitted.
*The Shach can be found here: http://hebrewbooks.org/pdfpager.aspx?req=9146&st=&pgnum=249