I have an c# application with two libraries ( moon-apns, tweetsharp ) .. Each library has a reference for newtonsoft.json.dll but different versions ... My app build success
Since you stated you have access to the source of the two libraries:
In both projects, set the reference to newtonsoft to not required Specific Version
. Rebuild those projects.
Now, when you build your main project, the two libraries should be ok with the same version of the newtonsoft DLL as long as there is no compatibility issues