Hmm, well, perhaps you could perform the myth about why the peacock has eyes on its feathers. 

Top!

You could do the myth of Cassiopea! This is one of my favorites! 

Greek myths! This actually sounds like a super fun assignment.

1. Tips for getting over stage fright. What works for me a lot is that I'm far better at telling stories than presenting information. So I don't memorize my speeches, I learn my concepts. Especially for stories like myths, if you're reacting off people (such as in a dialogue or a one-man-show where you're switching between characters) sometimes paraphrasing is okay and you can just make the conversation flow.

2. Greek myths: Theseus is a good one (the Minotaur, the maze, Ariadne). So is Perseus (Danaë, Medusa, Andromeda). Those are both rather long, though. You could do Cadmus (the dragon's teeth planted that became an army) or Bellerophon (taming Pegasus, fighting the Chimaera, flying to Olympus). And of course, there's always the option of picking a bit out of the Iliad. There are so many smaller stories to pick from there: the rage of Achilles (Achilles refuses to fight because of a conflict over a prize girl, mass destruction, he finally allows his friend Patroclus to fight, Patroclus slain by Hector, Achilles seeks revenge), Cassandra (cursed by Apollo to prophesy without being believed), Hermione (daughter of Helen and Menelaus), Aeneas (son of Aphrodite, went on to help found Rome and sire Roman emperors). 

Most of these aren't "origin" myths like Arachne (the spider) or Narcissus (the echo), but some of them are (of constellations). 

You could do the Cupid story. About how he came to shoot love arrows.

Hmmm...who's your favorite Greek hero?

We do that in my school, too!

Thanks for your help guys, my friend and I ended up performing the myth of Atalanta!