How to use GitHub API in Postman
Using the header method, you should be able to put "Authorization: token OAUTH-TOKEN" directly into the key input under the Headers section.
Obviously replace OAUTH-TOKEN with your actual token.
Edit: The above is correct, but I found it non obvious. The image shows what to do, (a) in the key field, put in 'Authorization', (b) in the value field, put in 'token '.
Looking at it in curl, it add -H "Authorization: token <your token here>" to the request, which is what is needed.