OS X Framework Library not loaded: 'Image not found'

So I managed to get it working, it's quite simple when you have the right instructions. What I was looking for was a 'private' framework which lives in the App bundle rather than being written to the system library folder.

Building The Framework

1. Add a target to create a Cocoa Framework
2. Within that targets 'Build Settings' configure the 'Installation Directory' to '@executable_path/../Frameworks'
3. Build library, and access the .framework from the archive or products directory

Including The Framework

1. Drag the created .framework file into the Xcode Project, be sure to tick 'Copy Files to Directory'
2. In the containing applications target, add a new 'Copy File Build Phase'
3. Set the 'Destination' to 'Frameworks'
4. Drag in the created .framework

[Xcode 11+]

The only thing to do is to add the framework to the General->Frameworks, Libraries And Embedded Content section in the General tab of your app target.

Make sure you select the 'Embed & Sign' option.

[Xcode v6 -> Xcode v10]

The only thing to do is to add the framework to the Embedded binaries section in the General tab of your app target.