You can create a newsletter by using a JSON like:
{ "description": "This is a test description. This is a test description. This is a test description. This is a test description.", "mainpage": "Foo", "publishers": [ "userName" ] }
and POSTing to the action=edit&title=Newsletter:Foobar with the right token to create a newsletter. You can see this in action from Special:ApiSandbox in your local install - with action=edit, and text = the JSON above.
This task is to unit test interactions with API edit on Newsletter namespace.
Tests in this direction can go to tests/content/NewsletterAPIEditTest.php