I'm kinda wondering if this would actually work with the audience who knows Superman's lore. It'd be like watching an episode of Blues Clues. "Gee, I can't seem to figure out why those nineteen whole bullets that absolutely hit him square in the chest didn't even slightly kill the guy." "HE'S SUPERMAN YOU CONSUMMATE DINK!"
All of the assassination attempts would need to involve less overt methods. Poisoning, pushing from tall buildings, etc. Most likely they'd need to outsource the jobs to mercenaries, since the CIA agents would figure it out immediately.
Edit: I wonder if my response just landed me on some list. Ugh...