Q. How do I cite and reference a conversation?

One of the purposes of referencing is to enable others, including your tutor, to find the information that you have used in your work. As it would not be possible for others to locate this type of source, you would need to add a transcript of the conversation as an appendix, and because of this you would not need to cite and reference them in the usual way.  Instead you would refer to the appendix in the main body of your work, e.g. (see appendix A).