Combine Cocoapods and Carthage

You can definitely make your framework available with both CocoaPods and Carthage. This is the path that I would recommend to allow your users to use whatever solution they prefer. Also note that setting a framework up to work with Carthage also makes it much easier for users who want to use your library without either of these solutions.

On a high level, for CocoaPods you'll want to create a podspec that lists your dependencies there. This way CocoaPods will manage downloading and configuring them along with resolving them against other user dependencies. See more here.

For Carthage you'll want to configure your project with framework targets for the platforms you support and add your dependencies in your Cartfile. More on that here

Combining both is actually not difficult. With my framework I have started with CocoaPods template containing Example and Pod directories. In the example project I created a new Cocoa Touch Framework target, made sure this target is Shared (in Product - Schemes - Managed Schemes) and dragged content of my Pod/Classes directory to the project (with unchecked Copy items if needed and added Target Membership only to this newly created framework).

This should be enough, Carthage should find this shared scheme and use it. Just keep in mind you have to commit changes and create a new git tag before using your framework from Carthage.