Your tama needs to be an adult and it needs the mirror. The mirror will show up periodically in the shop. I'm pretty sure this belongs in a nother section, but I hope that helps.
Im not sure, but I got the mirror before I got the make up and my tamagotchi used the mirror to put her make up on, so maybe you need both. (but my tamagotchi didn't like the make up anyway!!) :mimitchi: