In Agents of S.H.I.E.L.D. season 5, every police department has the pictures of the agents that are the most wanted (including Coulson), why didn't Tony Stark (with eyes everywhere) know about Coulson's situation.
Because Coulson is Schrodinger's Cat, he's both alive and dead.
In Agent's of S.H.I.E.L.D. he's alive (even if Tony Stark happens to visit).
In the MCU movie universe, he's dead.
Why? Josh Whedon says so.
“It’s a weird little yes and no. As far as I’m concerned in the films, yes he’s dead. In terms of the narrative of these guys [The Avengers] his loss was very important. When I created the television show, it was sort of on the understanding that this can work and we can do it with integrity, but these Avengers movies are for people to see the Avengers movies and nothing else. And it would neither make sense nor be useful to say ‘Oh and by the way remember me? I died!’”
The main MCU timeline/universe never saw Coulson return from the dead.
The book Marvel Studios’ The Marvel Cinematic Universe: An Official Timeline provides an official, chronological account of the events in the main MCU universe (also known as “616” or the “Sacred Timeline”). The book only mentions Coulson's death in The Avengers. It does not mention Coulson’s resurrection or the whole Agents of S.H.I.E.L.D. saga, implying that it never happened in the Sacred Timeline and that the TV show takes place in a different timeline.
Tony Stark doesn’t know that Coulson was resurrected, because it never happened in his timeline.
Spring 2012 | The Death of Phil Coulson
Loki escapes from his holding chamber when his minions board the Helicarrier. Natasha Romanoff battles the mind-controlled Clint Barton, hoping to snap her old friend out of his spell, and Agent Coulson confronts Loki with one of S.H.I.E.L.D.'s prototype weapons. Loki distracts him with an illusion and spears him through the chest with his scepter. "You're going to lose," a dying Coulson says. "It's in your nature … You lack conviction." After Loki's escape, Nick Fury uses Coulson's death (and the hero trading cards he doctored with blood) to inspire that sense of conviction in his perpetually clashing Avengers.
Phil Coulson's sacrifice is a defining moment for the Avengers.
Notice that the book's section about Coulson's death has the symbol for "Major Character Dies", suggesting that Coulson died for real.