The 1911 Census in Ireland produced evidence of possibly four families:Frederick and Catherine Knee  of Athleague Town Roscommon, Henry Frederick Knee and Louise Leonard Knee b abt 1855 of Eaton Square, Tenerure, Dublin, George Knee and Mary Jane Knee b abt 1877 of Ballindooloin, Carrick, Kildare, Simon Knee and Elizabeth Knee b abt 1884 of Paddock, Cavan.

A descendant of the “Knees in Ireland” has helped me with further information:

Frederick and Catherine were born and married in England before heading to Ireland to work on the Anglo-Irish estates. (The 1870s were particularly hard for English agriculture which suffered a Great Depression – a likely cause of emigration.)
Frederick Knee b.1845 in Seend, Wiltshire was the oldest son of Simon and Mary Webb Knee.
George and Mary Jane Knee of Ballindooloin, Carrick, Kildare and Simon and Elizabeth Knee of Paddock, Cavan are their sons. Frederick was the oldest son of Simon and Mary Webb Knee.  

I have traced Simon Knee using a combination of Ancestry BMD and Family Trees. Although I cannot get exactly the same line each time I try, all searches lead back to the common ancestor -Robert Knee of Bromham (1548) and his son William and Ann (Chandler) Knee.

Henry Frederick and Louise Leonard Knee are not of this line. It is my belief that Henry Frederick is also English and was born in 1855 in Stroud, Gloucestershire.

Apparently, around 25 people, surname Knee, nationality Irish, arrived in the US in the 1850s and 1860s. The majority sailed from either Liverpool or Glasgow. There is a puzzle here as there do not seem to be enough Knees living in either Ireland, Scotland or the north of England to supply 25.

O’Niadh which is pronounced O’Knee may have been the origin of the Irish ‘Knees’ who likely escaped to the US during the potato famine