Tony decides to mess with Phil by behaving. He doesn't realise that, within SHIELD, that's a form of flirting.
He decides it'll be funny to make Coulson wonder why he's had a sudden change of heart. Like switching the coffee to decaf until everyone gets used to it, and then replacing that with espresso. He starts paying attentions during briefings, and filling out his own reports, and even doesn't take out the suit unnecessarily for a while.
It works stunningly until he shows up in Coulson's office one day and finds himself in full-body contact with both Coulson and the wall. "Uh... what's going on?"
Coulson just smiles ever so slightly. "You know, if you really wanted to do this, you could have just told me. Clint and I have an arrangement. You didn't have to try to be subtle."
"Do what? What? You and Barton? I really did not need to know that you two are—an arrangement, you say?" Tony finds himself suddenly more interested in what might be going on, especially since he's getting first-hand experience of exactly how ripped Coulson is under that suit.
"Have you cleared this with Pepper?"
"Cleared... this?"
Coulson is already on the phone by the time the words finish coming out of Tony's mouth, still pressing him against the wall. "Hello, Pepper? Hi, this is Phil... Clint's doing great. He said to thank you again for that tip you gave him. Listen, is it all right with you if I borrow Tony for a few hours? He's been doing the office seduction thing. Do you want to talk to him? I've got him right here." He holds the phone out so Tony can speak with Pepper. "She wants to talk to you."
"Hey, Pepper. Do you know what's going on?"
She laughs. "Why didn't you tell me you were interested in Phil? It really doesn't take so much flirting to get through to him, you know."
"Pepper, I wasn't even aware that I was flirting. But yeah, now that you mention it... I am kind of interested."
"Good. Report back later." She hangs up, and leaves Tony trying to stare down Phil.
He's pretty sure he understands at least part of what Clint sees in Coulson by the time he goes home, sore in places he hasn't thought about in years.