The lowly citation 525s climb pretty fast. A long time since I flew one, but I remember seeing over 6000ft/min on CJ3 when lightly loaded. Even fully loaded it would do about 4500ft/min.
I was going to write that it must be the L39 Albatross (given that a number are in use as personal business jets around the world) but then I looked up the climb rate - only about 4200ft/min....