How to fix a permission denied (publickey) error for a git submodule update in the Github Travis CI build?

This can (thankfully) be easily solved by modifying the .gitmodules file on-the-fly on Travis, so that the SSH URL is replaced with the public URL, before initializing submodules. To accomplish this, add the following to .travis.yml:

# Handle git submodules yourself
git:
    submodules: false
# Use sed to replace the SSH URL with the public URL, then initialize submodules
before_install:
    - sed -i 's/git@github.com:/https:\/\/github.com\//' .gitmodules
    - git submodule update --init --recursive

Thanks to Michael Iedema for his gist from which I derived this solution.

If your submodules are private repositories, it should work to include credentials in the https URLs, I recommend making a GitHub access token with restricted permissions for this purpose:

# Replace <user> and <token> with your GitHub username and access token respectively
- sed -i 's/git@github.com:/https:\/\/<user>:<token>@github.com\//' .gitmodules