The German Alpine Club (DAV) tested several permanent marker pen inks (Edding 3000, Retract 11 and Staedtler Lumocolor) and found no reduction in rope strength in static tests. So I would feel pretty safe in using one of them, despite the fact that they are not specifically sold as "rope markers".
Roughly translated from German:
It makes sense to mark the middle of the ropes. Many rappelling and lowering accidents might habe been prevented by this. Marking the middle with tape makes little sense as the tape is not very durable and might slip. Additionaly, it might get stuck on the prussik when rappelling.
Using the inks Edding 3000, Retract 11 and Staedtler Lumocolor, no relevant reduction in strength could be found in static testing. They can be regarded as adequate to mark the middle of ropes.
Another longer Explanation for those who speak german.
The Edding company even promised the DAV that the name of the pen would change if the composition changed, so that the 3000 pen should be safe for the forseeable future.