Based on the post written here: https://sookocheff.com/post/tools/downloading-directories-of-code-from-github-using-the-github-api/

download_directory_from_git.py

import base64
import os

from github import Github, GithubException


def get_sha_for_tag(repository, tag):
    """
    Returns a commit PyGithub object for the specified repository and tag.
    """
    branches = repository.get_branches()
    matched_branches = [match for match in branches if match.name == tag]
    if matched_branches:
        return matched_branches[0].commit.sha

    tags = repository.get_tags()
    matched_tags = [match for match in tags if match.name == tag]
    if not matched_tags:
        raise ValueError('No Tag or Branch exists with that name')
    return matched_tags[0].commit.sha


def download_directory(repository, sha, server_path):
    """
    Download all contents at server_path with commmit tag sha in the repository
    """
    contents = repository.get_dir_contents(server_path, ref=sha)

    for content in contents:
        print "Processing %s" % content.path
        if content.type == 'dir':
            os.makedirs(content.path)
            download_directory(repository, sha, content.path)
        else:
            try:
                path = content.path
                file_content = repository.get_contents(path, ref=sha)
                file_data = base64.b64decode(file_content.content)
                file_out = open(content.path, "w")
                file_out.write(file_data)
                file_out.close()
            except (GithubException, IOError) as exc:
                print 'error processing %s: %s' % (content.path, exc)


if __name__ == "__main__":
    #put user and password here Github('USER', 'PASSWORD')
    GITHUB = Github('', '')
    USER = GITHUB.get_user()
    #put repo name here
    REPO = USER.get_repo('REPO_NAME')
    #enter branch name here
    SHA = get_sha_for_tag(REPO, "BRANCH_NAME")
    #put directory name here
    DIRECTORY_TO_DOWNLOAD = "SOME_DIRECTORY"
    os.makedirs(DIRECTORY_TO_DOWNLOAD)
    download_directory(REPO, SHA, DIRECTORY_TO_DOWNLOAD)

This is something I was testing for an aws lambda function I was going to try. I don't think I'll actually use it now.
Maybe it will be useful to someone.
Putting the credentials and other variables in like this isn't ideal so I'd re-work that a bit if you want to use it.

The changes I made to the code from the blog are to maintain the directory structure. I also didn't want to have user input since I wanted to use it for a lambda function.