My co-supervisor wants authorship in a paper he didn't contribute
Most journals have authorship policies. These are recommended by the International Committee of Medical Journal Editors (http://www.icmje.org/recommendations/browse/roles-and-responsibilities/defining-the-role-of-authors-and-contributors.html), among others.

The Committee on Publication Ethics (COPE) has guidance on how to avoid authorship disputes. https://publicationethics.org/files/2003pdf12_0.pdf

Be factual with your supervisor. Provide the authorship guidelines and ask him to list his contribution to the research article. You can explain that the culture on authorship has changed and that automatic authorship for higher level supervisors is no longer considered appropriate by publishers (as evidenced by the guidelines of the publication). Truthfully, it would be best if your host supervisor perform this deed because they are on an equal footing and apparently had some prior connection. Clearly, it puts you in a difficult situation.