The guys from SwiftyJSON, have been taking a bit longer to merge pull requests. So, as it stands, you can't use it with Swift 2.0 and Carthage, but since a pull request exists to fix that, you can:

  1. Fork the project.
  2. Go to the pull request's owner repo and create a pull request from his branch to your own copy.
  3. Merge the pull request into your repo.
  4. Congratz, you just fixed the issue. ✨
  5. Add github "RuiAAPeres/SwiftyJSON" >= 2.2.1 to your Cartfile.

On the long term this is not practical, but for now it will do.