I'm sorry but I don't have any information for you, my family I'm researching are the Downings - a female Nesbitt married into the Downing family hence the link.
The house Tubberdaly, outside Rhode, King's County/Co. Offaly was burnt down 2 a.m. 15th April 1923. You can see information on the house if you Google Toberdaly House and look for www.buildingsofireland.ie
- its the National Inventory of Architectural Heritage.
I also found a Connor family in Toberdaly but I don't know if it's your Connor family. They are in the 1901 census www.census.nationalarchives.ie
They may be too late.
The father is Edward Conner aged 55 and there is a daughter named Annie aged 24 who is described as a general domestic servant.
Hope some of it helps,