Well, IMDB is wrong — Bryan Cranston's father Joseph L. Cranston was born in Illinois in 1924-1925 and raised in Chicago, according to the 1930 census (the IMDB reference to Iowa has disappeared :-).
Joseph's father was Edward B. Cranston, also born in Illinois in 1896-1897.
Edward's father was named James Daniel and was born in Montreal, Canada in 1849.
Daniel's father was named Joseph Henry and was born around 1826 in Armagh, Ireland. From Canada he immigrated to the US and served in the Civil War, surviving that and dying in 1889 in a Dayton, OH soldier's home.
No more information, unfortunately. But it turns out this is Pamela Cranston's family, and she provides further interesting details here that are in contradiction to some of what the TV program says:
http://boards.ancestry.com/surnames.cranston/119.1.2/mb.ashxhttp://boards.ancestry.com/surnames.cranston/134.2.2.2/mb.as...There are a number of other people who may see this message who have roots in Armagh, sometimes with the name of Joseph and James, but I believe they are later than 1826.
This is also in the neighborhood of my family in eastern Tyrone, so there could be a connection there. But again I have no information on how they might be related.