Hmm...the 1911 census is for New Monkland South.
Ann Kennedy, Head, 69, born Ireland
Arthur, son, Wid, 32, born Carnwath
Cornelius, son, single, 31, born Carnwath
Eliz, grandaughter, single, 16, born New Monkland.
My Cornelius did have a sister Annie but she was born in 1860, Carnmoney, Ireland which would make her around 51 in 1911.
I can't get any other search result for the 1911 census for Cornelius and Susan Kennedy. I know for sure they were living in Kirk Road, Wishaw in 1907 & 1908 when their first and second children were born as I have just viewed the images. 1910 still shows them living in Cambusnethan/Lanark area when their next son was born - I viewed the index but don't have enough credits to view the actual certificate at the moment. I'll buy more credits later.
I can't be sure they moved from the area around the 1911 census - I know they were still in the area when they died in the 40's.