Is there a way to change your twitter password via the python-twitter API or the twitter API in general? I have looked around but can't seem to find this information...
Fortunately not!  Passwords are very confidential information which only Twitter itself wants to handle.

Think about a third-party developer suggesting to change your Twitter password:

would you trust them and let them see your new password?
how could you make sure they are really going to set your new password and not another one?
Password Change with the Twitter API