I know I've answered this question before (or maybe it was @SessionScoped
, same thing really). The Conversation is tied to a Session in CDI. As there are no Sessions in JAX-RS there are no conversations. In the spec section 6.7.4 it states that the Conversation scope is only active during JSF requests.
If you would like to create your own Scope and Context that acts like the conversation one and make it available to JAX-RS requests, that's certainly doable, but you'd have to have some location to store the scope and also associate it with a request.