Coni is the deputy director of the Government Communications Service, working out of the Cabinet Office and Downing Street. He leads on issues of professional capability and training for the more than 3,500 government employees who make up the GCS.
Brown, the CIPR's president for 2016 and a founding director at Manchester agency Rule 5, said the appointments would "elevate the status of the CIPR in the eyes of members and non-members alike".
Byrne said: "Along with the PRCA, whose board I have been part of for some years, the CIPR has a crucial role to play in professionalism and reputation in our industry and I would like to give that whatever support I can."
The CIPR's nine-person board also includes 2015 president Sarah Pinch and 2017 president-elect Jason MacKenzie.