No one is arguing or stating that a SIC "type rating" is required for domestic flights. The OP wants to know how to go about training a SIC (so that he/she may legally log the time) in a Cessna 550.
FAR 61.167 states (in part):
Sec. 61.167 — Privileges.
(a) A person who holds an airline transport pilot certificate is entitled to the same privileges as a person who holds a commercial pilot certificate with an instrument rating.
(b) An airline transport pilot may instruct—
(1) Other pilots in air transportation service in aircraft of the category, class, and type, as applicable, for which the airline transport pilot is rated and endorse the logbook or other training record of the person to whom training has been given;
(2) ..................