The concept of a coroutine sounds very interesting, but I don't know, if it makes sense in a real productive environment? What are use cases for coroutines, where the coroutine implementation is more elegant, simpler or more efficient than other methods?
True coroutines require language support. They need to be implemented by the compiler and supported by the underlying framework.
One language-supported implementation of coroutines is the C# 2.0 yield return keyword, which allows you to write a method that returns multiple values for looping.
The yield return does have limitations, however. The implementation uses a helper class to capture state, and it only supports the specific case of a coroutine as a generator (iterator).
In a more general case, an advantage of coroutines is that they make certain state-based computations easier to express and easier to understand. For example, implementing a state machine as a set of coroutines can be more elegant than other implementations. But doing this requires language support that doesn't yet exist in C# or Java.