In a food processor with a metal blade, process the sugar and coffee powder until the texture of the sugar becomes very fine.
In a large mixing bowl, beat the egg whites and vanilla extract with an electric mixer at medium speed, until very frothy. Add cream of tartar, and continue beating at medium speed until soft peaks form. Increase beater speed to high, and gradually beat in sugar-coffee mixture. Continue beating until soft peaks form and mixture has a glossy sheen.
To pipe cookies from pastry bag: fill pastry bag (or 1-gallon freezer bag), fitted with Number 6 plain round pastry tube, with meringue.
Hold bag upright over prepared cookie sheets and squeeze out meringue, leaving pastry tip buried in meringue, until you have piped out a round about 1 1/2" in diameter. Lift up tip and stop squeezing.
Leave 1" between cookies. Or, drop by tablespoonfuls onto prepared cookie sheet, leaving 2" between cookies.
Bake for 1 hour without opening oven door.
Turn off oven, and let meringues dry in oven 2-3 hours more without opening oven door. (After the first hour, it's okay to peek just once.) At this point you can leave them in the oven overnight.
Remove the meringues from the cookie sheet with a spatula. Store in airtight container.
