Looks like this post has been flying under the radar, I hope you've found the answer already! To close the loop for the community, As of today, the Tableau REST API only supports username/password authentication, explained in detail here: Authentication-Tableau Server REST API - Tableau. That said, hard coding credentials is not ideal and it's why we have personal access tokens coming soon (Coming Soon: New features in Tableau):
While this feature is not GA yet, it should be available in a newer version of Tableau Server soon. Please let me know if you have any questions.