Ways to make your liquid eyeliner stay is don't touch it, or rub any where near your eyes until it dries. As this is true, you can try to take blush or foundation and lightly put it over your liquid eyeliner so you have a barrier between your eyeliner and finger when you rub your eyes.
You can try using an eyeshadow base, which are supposed to prevent smudging and are inexpensive.
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Try the brand, Slick Writers. It's known for not smudging on
paper, including photos, stickers, ribbon, vellum, metal and glass.
See the 'Related Links' below for a link to purchase Slick
Writers.