You can simply pass nothing to the main class, to use the API without authenticating.

from github import Github

g = Github()
r = g.get_repo("REPO_USER/REPO_NAME")

I ended up solving it by getting the "authenticity token" from the GitHub login page first, and then posting it:

import requests
from pathlib import Path
from github import Github
from bs4 import BeautifulSoup as bs

auth = 'username', 'password'
asset = Github(*auth).get_repo('user/repo').get_latest_release().get_assets()[0]
user_agent = 'Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/77.0.3865.120 Safari/537.36'
headers = {'user-agent': user_agent}
login_url = 'https://github.com/session'
session = requests.Session()
response = session.get(login_url, headers=headers)
authenticity_token = bs(response.text, 'lxml').find('input', attrs={'name': 'authenticity_token'})['value']
session.post(
    login_url,
    headers=headers,
    data=dict(
        commit='Sign in',
        utf8='%E2%9C%93',
        login=auth[0],
        password=auth[1],
        authenticity_token=authenticity_token
    )
)
# Now I'm logged in properly, I can download the private repository assets
response = session.get(asset.browser_download_url, headers=headers)
save_to = Path.home() / 'Downloads' / asset.name
save_to.write_bytes(response.content)

Here is the code example:

400: # Continue on errors. continue; for artifact in json.loads(artifacts)['artifacts']: if "StartingFileName(ChangeThis)" in artifact['name']: filename = f"{artifact['name']}.zip" print(f"Downloading {filename}...") status, headers, response = run._requester.requestJson("GET", artifact['archive_download_url']) if status == 302: # Follow redirect. success = urllib.request.urlretrieve(headers['location'], filename) break if success: print("Success!") break">

import base64
import json
import urllib.request
from github import Github
from pprint import pprint

g = Github()
repo = g.get_repo("Repo/Example")
success = False
for run in repo.get_workflow_runs(branch="main", status="success"):
    if run.raw_data['name'] == "Workflow Name (ChangeThis)":
      status, headers, artifacts = run._requester.requestJson("GET", run.artifacts_url)
      if status > 400:
        # Continue on errors.
        continue;
      for artifact in json.loads(artifacts)['artifacts']:
        if "StartingFileName(ChangeThis)" in artifact['name']:
          filename = f"{artifact['name']}.zip"
          print(f"Downloading {filename}...")
          status, headers, response = run._requester.requestJson("GET", artifact['archive_download_url'])
          if status == 302:
              # Follow redirect.
              success = urllib.request.urlretrieve(headers['location'], filename)
          break
      if success:
        print("Success!")
        break