FAR61.51 - (f)
Logging second-in-command flight time. A person may log second-in-command time only for that flight time during which that person:
(1) Is qualified in accordance with the second-in-command requirements of §61.55 of this part, and occupies a crewmember station in an aircraft that requires more than one pilot by the aircraft's type certificate; or
(2) Holds the appropriate category, class, and instrument rating (if an instrument rating is required for the flight) for the aircraft being flown, and more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is being conducted.
61.55 is too big to post, so here's the link:
61.55
As I read it, to log SIC part 91, the A/C must require an two pilots. If your CJ2 capt
has the single pilot type rating, then you're not required and thus cannot log SIC time. If he
does not have the single pilot type, then you ARE required and must meet the above requirements (SIC type or AMEL/Inst). However, if you're NOT required, and the PIC has an MEI, then you can log dual received. (I think you can log dual received even if he doesn't have an MEI as long as he doesn't exercise MEI privileges such as single engine training). Your Capt should know his limitations as a CFI and what he can legally log as dual given.
As far as I know, the CJ2 is a single pilot airplane, but the PIC must have a Single-pilot type rating. I'm pretty sure the Eclipse is the same way.
Hope this helps.