Prison Service director general Colin McConnell said: "Yesterday's tragic events at Hydebank Wood have stunned everyone and there is deep sadness across the service."
The service said the deaths would be investigated by the police, coroner service and Prisoner Ombudsman.
Just after 5pm yesterday during the unlock of offenders in an area known as Elm 1, officers found Mr Carson collapsed in his cell. They tried to resuscitate him but he could not be revived. A ligature was recovered from his cell.
At around 8.30pm last night during a routine check by staff in a part of Hydebank known as Ash 4 and housing women prisoners officers found Ms McKeown collapsed in her cell. Efforts by staff and paramedics to revive her were unsuccessful. A ligature was also recovered from her cell.
Mr McConnell added: "At this very difficult time I offer my sympathies to both the Carson and McKeown families. They are in the thoughts and prayers of our entire service.
"I also want to recognise the efforts made by the staff who were on duty at the time, who did everything they could to bring about a different outcome."
According to Prison Service annual reports, during the year 2009/10 there were 190 incidents of self-harm across all sites as well as one death in custody awaiting an inquest.
In 2008/09 there were three deaths in custody awaiting inquest. In 2007/08 there were two deaths in custody awaiting inquest, and in 2006/7 there was one death in custody awaiting an inquest and one confirmed suicide.
In July 2008, Colin Bell, 34, hanged himself at the high-security Maghaberry prison, Co Antrim, while on suicide watch.
Officers slept while they were supposed to be monitoring him, an independent investigation said. The inspection team appointed by the government recommended a number of changes to the prison regime.
Hydebank accommodates all young male offenders aged between 17 and 21 years on conviction, serving a period of four years or less in custody, and all female prisoners including young offenders.
Women transferred from Mourne House, Maghaberry, to Hydebank Wood in June 2004. Female immigration detainees are also held in the unit.
The governor at Hydebank is Gary Alcock and he has 382 staff to deal with 306 prisoners in single-cell accommodation, the Prison Service website said.
The service has a suicide and self-harm prevention policy which aims to identify those potentially at risk, encourage vigilance by staff and ensure the inmates are managed by skilled people and treated appropriately.
The policy includes reviews of the physical environment to reduce the opportunity for suicide, as well as anti-bullying measures.
Both inmates were on remand awaiting trial. Carson, from Hesketh Road, Belfast, appeared at Belfast Magistrates' Court in March last year charged with raping and sexually abusing a girl aged 15 over three days. He was also charged with making indecent images of a child on the same dates.