I\'m working on a Scheme interpreter written in C. Currently it uses the C runtime stack as its own stack, which is presenting a minor problem with implementing continuation
Patrick is correct, the only way you can really do this is to use an explicit stack in your interpreter, and hoist the appropriate segment of stack into the heap when you need to convert to a continuation.
This is basically the same as what is needed to support closures in languages that support them (closures and continuations being somewhat related).