According to the ABC Island of Ireland report, The Sunday Business Post's circulation was up 2.1% year on year to 54,993 copies and the Independent News & Media-owned Sunday World experienced a modest rise, up 0.5% year on year to 285,214. Northern Ireland's Irish News' circulation increased 0.1% to 47,819.
The gloomy picture elsewhere was blamed on the recession and continued growth in news online.
Andrew Sinclair, deputy managing director, OMD Ireland, said that as the penetration of broadband continues to rise, he expects circulations to continue to fall - but this did not need to be a bad thing for the industry.
Sinclair said: "Digital properties give consumers a new opportunity to consume the product online. We're a couple of years behind the UK, but online is becoming an integral part of media plans."
Oliver Keenaghan, general manager, News International Newspapers Ireland, said the recession has hit the circulations of Irish papers. "You have to take it in context of the Irish economy, which has been in recession for six months," he added. "Consumers are making conscious decisions about where to spend their money."
The Irish versions of British papers do not feature in the report, but, according to ABC data from December for 2008, the circulation of the Irish edition of The Sun between July and December averaged 99,646, down 6.94% year on year, but increasing its market share by 0.69%.
Alongside the Irish News, six non-daily Northern Irish titles posted circulation rises year on year. The title with the largest circulation is the free Belfast News, up 2.9% to 47,446.
Despite circulation declines, the Irish newspaper sector is still strong with a high level of brand loyalty. Rachel Littlewood, account director, MediaCom, said "in terms of coverage of the audience, newspapers are a fantastic way of getting to everyone".
The Irish magazine market faces tough competition from the British titles, which have larger budgets, higher profiles and larger staff. The free magazine, Skymag, remained the largest magazine by circulation at 518,974, up 14.2% year on year.
Karen Hesse, joint managing director, Dyflin Publications, which publishes House and Home, said: "A recession is a time to be innovative. How you set yourself aside from your competitors will determine whether you will hold your position."