Drupal 6 with custom OAuth Server
Drupal 7 has the oauth2_server module that allows you to run an OAuth2 server. It is well documented and integrates a well known and stable PHP library.
OAuth2 is probably a better option for you than OAuth1 because it has grant types optimized for different usage scenarios (mobile app, web app, etc).

If you're limited to Drupal 6, your only option is the OAuth module (also available for D7), but keep in mind that Drupal 6 is basically a deprecated version so when it comes to contrib support and bug fixes you are pretty much on your own.