I have a James Kneale who lived nearby on Bigwell Street (now the car park that Frances mentioned). James Kneale was born Sept 28, 1812 in Douglas and married Anne Boyne on April 25, 1849. They had three children: James Kneale 1849, Thomas 1842, and Ann in 1851.
Nigel Crowe (I think) researched a nearby property on 7 John Street in Douglas that is the oldest house in Douglas, and currently the site of "Scotts Bistro". A plaque in front reads "...In 1844 Thomas Kneale bought 7 John Street for 270 pounds from William Lloyd. The Kneales kept the house until 1898...". I don't have any links to those Kneales, but perhaps you do. If so, you might enjoy warming yourself by the same fireplace as your ancestors some time.