I\'ve just declared a constant for the \"application/json\" content type in one of my classes.
public const string JsonContentType = \"application/json\";
In order to add an up-to-date answer: since dotnet core 2.1 MediaTypeNames.Application.Json has been defined.
MediaTypeNames.Application.Json
See https://github.com/dotnet/corefx/pull/26701 for the changeset.