There are few options you can use. First, leverage APPVEYOR_SCHEDULED_BUILD and APPVEYORenvironment variables. As an option you can check if both variables value is True, ignore them. Here I assume that AppVeyor run those tests automatically. If you run them as a test_script, you can condition your script to use those variables (or just APPVEYOR_SCHEDULED_BUILD as you probably do not run script on local machine).
Also you can create separate project targeted the same repository specifically for nightly builds and configure it separately. Disadvantage of this approach is separate build history. Also another project for the same repository will have URL slug with random ending. This you can change with API call (script sample).