There seems to be ongoing confusion over SP operations in Cessna Citations. The CJ series, CJ-1, CJ-1+, CJ-2, CJ-2+,CJ-3 can all be flown single pilot. They are FAR23 certified aircraft, built to FAR 25 standards. As such they can be flown Single Pilot on Private and Commercial operations. They max takeoff weight of the aircraft has no influence on the SP certification
The C-500, C550/C560 (Citation II, S550, Bravo, V, Ultra and Encore) are Part 25 certified aircraft and require two pilots. However you can obtain a SP waiver after completing a checkride in accordance with FAA waiver 4050. Such operations are limited to Private flights because they are Part 25 aircraft.
C-501 and C-551 were factory certified Single Pilot versions of the Citation I and II and as such can be flown commercially by one pilot.
Different countries may impose higher requirements, and not accept the FAA certifications. If your aircraft is certified single pilot but you fly it commercially with two pilots then both pilots can log the time (Command - Co-Pilot) if you have appropiate two crew training and procedures in your company operations manual.
As far as the CJ series in concerned I believe that something like 70% of the aircraft are owner flown. I recently attended Flight Safety for C-208 Caravan training and there was quite a few people in for SP two year recency, especially for the Ultra and the Encore.