You should be able to move these reports to the artifacts directory and then use the artifacts API (http://confluence.jetbrains.com/display/TCD8/REST+API#RESTAPI-Artifacts) to return the reports.
For example to access an MSTest report you can add the following line to you Artifact Paths
:
%teamcity.build.checkoutDir%\**\*.trx =>
This will copy all files with the extension trx
to artifacts directory (any sub-directories they are contained also be copied). You can then use the following REST API URL to download the report/s (replacing the <...>
placeholders with actual values):
http://<TEAMCITY LOCATION>/httpAuth/app/rest/builds/<BUILD ID>/artifacts/content/<REPORT PATH>
For example with the following URL,
http://teamcity:1234/httpAuth/app/rest/builds/5678/artifacts/content/testResults/MSTest.trx
It will return the file with the artifact path testResults/MSTest.trx
for the build id 5678
from the TeamCity server located at http://teamcity:1234
.