Accessing data from the Cobertura plugin via the REST API is not possible.

Hitting the URL http://<jenkins>/job/<name>/<build>/cobertura/api/xml gives:

<coverageResult><results/></coverageResult>

and .../api/json gives:

{ results: { } }

If either depth=2 or appropriate tree argument is given, data is returned, but not all information that is seen on the html pages. Specifically the totals (e.g number of lines) used to generate the ratios is missing. Because of this one cannot determine the relative sizes of the components or the overall size of the project.