I just created my first private channel, and I wanted to know if there is a way to prompt a user to input a password before they can add the channel
No. But since you need to know the install code to add the channel, that effectively is a password. There's no list of private channels published, so only the people you give the code to will know it.
Actually there are a number of private channel directories
On the Internet. Just Google ROKU private channel listings