No, CoAP don't have cookies. A cookie is related with the browser not with the protocol. However CoAP uses a Etag, which could be seen as an alternative to a cookie.

An entity-tag is intended for use as a resource-local identifier for differentiating between representations of the same resource that vary over time. It is generated by the server providing the resource, which may generate it in any number of ways including a version, checksum, hash, or time. An endpoint receiving an entity-tag MUST treat it as opaque and make no assumptions about its content or structure.