Willie,
If you have a Far/Aim check out the 135 instrument SIC Mins. Off the top of my head I think you need 500 hours tt and a certain amount x-c and so on.
If you want to fly the citation. you have to find out what the companies insurance mins are. for jets there usually high but exceptions can be mad if you have connections. most citations require 2 pilots but some line a ce-500 only require one. you do not need a type to fly sic, but you have to have a legit 135 company check. you have to find out if this company hold their own 135 cert or some other co has it.