I want to allow people to clone my private repository by using a password, even if they are not Github users. Is that possible?
No, that's not possible. GitHub restricts access based on usernames and doesn't provide anonymous access to private repositories using a password. Anyone who wants to clone your repository from GitHub will need to have their own account and will need to have been added with read permissions on the repository.
Alternately, you can set up a mirror on a server you control with Git and a web server and give out the password there.