Fury said Coulson died believing in heroes. He never said he stayed dead.
My best friend died 25 years ago. Twice. I was talking to him this week. He died on the operating table after a car accident. They brought him back. It didn't take and he died again. They brought him back again. This time it took.
Modern medicine can work miracles. Not always, but often enough.
Coulson dies, the med-techs arrive and get him to Emergency. The docs hook him up to a heart machine to keep him going while they repair the damage to his own heart. He's probably in ICU for months, then rehab for even longer. But in the end Phil Coulson walks out of the hospital under his own steam.
My guess is that in the pilot episode he's just now returning to duty.
Is this really so difficult a concept to grasp?