I used crayon once and put them under my broody duck hen. The crayon was gone by the next day. I try to only use pencil now but have used markers too, permanent and washable.
I've used perminant marker and pens, however, because egg shells are porous, they do seep into the pores and there is always that slight risk of being bad.
I use edible markers. You can get them at cake supply stores. They're food coloring, but write and look like permanent marker. And, If you have kids, they're fun to use afterwards on all sorts of stuff!