You can try this type of Authentication witch is pretty basic:
Here you have a sample Request:
POST /accounts/ClientLogin HTTP/1.0
Content-type: application/x-www-form-urlencoded
accountType=HOSTED_OR_GOOGLE&Email=jondoe@gmail.com&Passwd=north23AZ&service=cl&
source=Gulp-CalGulp-1.05
Note that this type of authentication has been deprecated.
Note: The YouTube Data API (v2) has been officially deprecated as of March 4, 2014. Please refer to our deprecation policy for more information.
Important: The ClientLogin authentication protocol has been officially deprecated as of April 20, 2012. It will continue to work as per our deprecation policy, but we encourage you to migrate to OAuth 2.0 authentication as soon as possible. If you are building a new application, you should use OAuth 2.0 authentication.
If you are already using ClientLogin and are encountering authentication failures with certain accounts, refer to the ClientLogin #FAIL blog post for recommendations.