TeamCity provides its own NUnit test launcher, which can be easily configured via web UI for MSBuild and Visual Studio (sln) runners. You can set up NUnit testing options while creating or editing Build Configuration and TeamCity will run them and report the results. You do not need to configure the tests in your build script, neither you need to have NUnit runner.
To set up NUnit tests, do the following:
While creating/editing Build Configuration, go to the Runner page.
Select the desired build runner: MSBuild, or Visual Studio (sln).
Enable Run NUnit tests option.
Specify the properties to be passed to the TeamCity NUnit test launcher, such as Tests platform, Tests run framework, NUnit runner, etc.
Continue with editing other Build Configuration settings.
note
If you need to use third-party NUnit addins, consider using TeamCity NUnit test launcher from command line, where it is possible to pass the list of the addins as an option.
When configuring TeamCity NUnit Test Launcher via UI (as well as when using it via command line, or from the build script tasks) you can set up .NET Code Coverage in few clicks at the same Runner page.