There's a reason Coulson is Cap's biggest fan - it's because he always wanted to be like him, and in a way he became him. Those Captain America cards Coulson collected? What if the "vintage" set is his from when he was a boy during WWII?
Coulson's character fits all of the requirements Dr. Abraham Erskine (Stanley Tucci) outlined in explaining to Rogers (in Captain America: The First Avenger) why he chose him to be the one man to get the super soldier serum, so what if Coulson got some other version of it later, after Cap disappeared (we know the military still wanted a super soldier serum. See: Hulk)?
Fun fact: the kid in Captain America: The First Avenger who sports the painted garbage can Cap shield is named Phil. The serum explains the slower aging. Hat-tip to Jane.
Verdict: A great idea that's true to the character. Why it's being kept secret from Coulson we have difficulty explaining unless it's something SHIELD isn't proud of because something went wrong.