Eyes Black/brown eyelashes vs white eyelashes

I wouldn't recommend using a marker as it could end up seriously staining your doll!

 

Best bet is to just replace the lashes. Trying to stain them with anything is a big risk to the doll itself.

 

You might also end up with super clumpy eyelashes. Going to second everyone else... carefully remove the current lashes and replace them with something in your preferred color. If you're in the US, you can order them from Volks USA or possibly other shops that sell items for other doll types.

 

Eyelashes almost always get put on last, after the rest of the faceup is sealed, so as long as you're gentle removing them won't cause any damage to the faceup. Typically they get put in with school glue or something like it, so it doesn't take much effort to get them to come out.

Doll eyelashes are fairly cheap online; Alice's Collections has different types for $2-$5 USD. If you don't want to wait for shipping times, you can also use human false eyelashes! It may take some playing around with those to get the scale right, but you can get them in your hands immediately by visiting the drugstore of your choice.

If you're curious about whether or not your marker dye method would work, you could always try buying some white doll eyelashes and experimenting with them out of the doll. I know Alice's has white lashes since I got some from there before, for a non-human doll in my collection.

 

For slight tinting of light color eyelashes without removing them I have used alcohol markers.

A summary of the process:
To protect the dolls face from any possible marker slips, wrap the top and bottom with scraps of cling wrap leaving just the eyelash area open.
Touching a few of the individual the lashes with the tip of the marker, pull the marker stroke out away from the dolls face along the lash's length.
Repeat until all desired lashes are covered with the color or colors of choice.
Let dry completely.
Alcohol dries fast, but give it a good 3 to 5 minutes between coats if the color is not dark/intense enough for your liking. Don't put down more than a few coats on plastic lashes, they don't keep the color as well as natural materials.
If you do slip and get alcohol marker on the doll's eye drop some clear alcohol on a Q-tip/cotton bud and gently wipe it off. Dampen the other end with a tiny bit of water to wipe the remaining alcohol off. Let dry.
Unwrap the dolls head when done.

Notes: I used Sharpies, but if you have Copics or another alcohol-based marker those could work too. If you have some loose bits of the same color eyelashes laying around to test on please do so. To get the best idea of how it will work use tweezers to hold up short sections of lashes and paint the color on while they aren't resting on another surface. This will tint the lashes a good bit but won't turn white lashes into black lashes.

 

I dyed a synthetic wig with alcohol ink. I found that Molotow ink had the best coverage of the brands that I tested. Most of the other brands just rinsed away. I suppose the same will be the case for synthetic eyelashes as well.