Harp strings may be supplied pre-coloured, red for C, black for F. If the colour is integral to the material (nylon or Nylgut) it will be permanent. The colouring on gut strings can wear away over time.

I presume the autoharp would have wire or wire-wound strings? Sharpies as suggested above would achieve the same effect, but may require refreshing from time to time.I cannot imagine that the ink would significantly affect the tone. Paint would not be a good idea.

Ross