If you read the FAR's about logging SIC time, it says (I'm paraphrasing from memory, so do your homework...) you basically can log all the time you performed SIC duties in an airplane type certificated for more than one pilot, or if the operation's laws require more than one pilot, provided you've received the training required and done your 3 takeoffs and landings.

So, even though the pilot may have a single pilot authorization, that's something HE/SHE has, not the airplane.

I'm assuming here that the CJ2 and the Eclipse are 2-pilot airplanes, I don't actually know.

I was in the same boat a while back while doing some right-seat time in a citation SII with a pilot who had a single pilot authorization. As others have said though, know the systems for whatever airplane you log time in, and be able to answer questions about its operation, limitations, etc..