I don't use MySpace but, to the best of my knowledge, it doesn't host videos on the MySpace server. The only option that it offers is to 'embed' videos. This means that you have to put the video on another server, such as YouTube, and then paste HTML text into your MySpace page so that the video is called from the YouTube server.
YouTube allows you to post private videos but they can only be viewed by people who you've mailed an invite to. (Actually, there's a way around this, so YouTube private videos aren't really as 'private' as they're meant to be). If you try to embed a private video into a MySpace page it won't display.
Your best option is probably to post the video on a site which allows you to password protect access to it. Most video sharing sites don't offer password protection. Among those that do, it's very hard to find a site which offers a working embed code for sites like MySpace. However, Vimeo should meet your needs. If you put a password protected video on their site, and then post the embed code onto MySpace, the viewer will be prompted to enter a password. You can either mail the password to potential viewers or, if you're happy for everyone who accesses your MySpace page to see the video, simply publish the password alongside the video link on your MySpace page:
http://www.vimeo.com
Chris