Where do I find my EC2 private key?
Ok, turns out that I need to generate a new X.509 certificate, and then I'll be able to download both the EC2_PRIVATE_KEY and the EC2_CERT files.
This link proved useful: http://paulstamatiou.com/how-to-getting-started-with-amazon-ec2
The private key is only downloadable at the moment you create the certificate.