Heat oven to 375 F. Line baking sheet with parchment paper.
Measure egg whites. If they aren't quite ½ cup, add a little water to reach that level. Then add the vanilla, liquid sweetener, and water so that sweetener and water together equal 2 Tablespoons.
Mix in unsweetened coconut. The mixture should just hold together. Let set a minute or two and you'll be able to mold them better.
Roll into balls a little bigger than an inch in diameter. Slightly flatten and put on baking sheet (whatever shape you put them in is how they will stay, so this is your chance). Put at least half an inch apart.
Turn down the oven to 325 F, and bake for about 15 minutes, but start checking them a couple of minutes before. You want them golden brown on the bottom, and just barely starting to brown on top (though if you like them a little crispier, bake a couple of minutes longer).