The best replacement for sharpie is fabric marker.

The best alternatives to sharpie are rated as following:
★★★★★  fabric marker
★★★★★  bic mark it
★★★★  copic
★★★★  porcelain pen
★★★  prismacolor
★★★  posca
★★  staedtler
★★  artline
★★  laundry marker
★★  dory
★  skerple
★  bic
★  permanent marker
★  shoupie
★  rubadub sharpie
★  magic marker
  marker

Your alternative for sharpie is not listed? Suggest!
Speaking about sharpie, one probably shouldn't forget about watercolor.

Other search terms related to sharpie and their ratings are:
★★★★★ watercolor
You have in mind a companion for sharpie and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of sharpie in all years. Click on graph for more.
sharpie
fabric marker
bic mark it