This is a long shot, but I see that Timothy had a son James born in 1820. I am looking for a James Hannigan and wife Bridget who had a son Patrick Joseph Hannigan in New York City on May 29,1850. Parents and son relocated to Brantford, Ontario, Canada where they are recorded in the 1871 census. From their ages on the census it would appear James was born in Ireland about 1815 and Bridget about 1817. Do you know if this could be your James?