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.
(..) She'd lift him and hold him and let him drop. Boom! ''Jeffrey, Jeffrey,'' and Jeffrey would (imitates crying) ''Jeffrey, be quiet.'' And then Jeffrey would cough. (imitates coughing) People began to hate Jeffrey. One gentlemen invited Jeffrey into the men's room to play with the blue water. (..)1983 Bill Cosby: Himself