The police made the suspect 'cough up' the names of his accomplices.
They 'coughed up' [='lost, gave up'] the lead in the second half.
We had to 'cough up' an extra hundred dollars for the car rental.
(..) He's very smart. He's one Yeah, it's OK. Go talk to him. - What are you watching? - Bert and Ernie. Forrest, I'm sick. What, do you have a cough due to a cold? I have some virus, and the doctors, they don't know what it is, and there isn't anything they can do about it. You could come home with me. (..)1994 Forrest Gump