Murdoch MacLennan, chief executive of the Telegraph Media Group, said Mr Coulson, who is also a former Downing Street communications director, always behaved "professionally".
Foreign Office minister Baroness Warsi said Mr Coulson offered "clear advice" in his time at No 10, ahead of her appearance on Question Time alongside BNP leader Nick Griffin.
In a written statement read out at the Old Bailey, London, Lady Warsi said: "He was very much a team player. He was always happy to take time if you needed his help."
Mr MacLennan said Mr Coulson was a man of "integrity and honour".
Mr Coulson and six other defendants all deny hacking charges. A change has been made to the indictment, with the word "conspiracy" removed from count seven.
It means the defendants are charged with perverting the course of justice. Judge Mr Justice Saunders said the changes were "technical" and did not elaborate.
The trial continues.