I have just found this forum and posted the following:
In researching my family, I have found a family of Denning/Dennin/Dinnin/Dineens (the spelling depends on the source), who emigrated from Ireland to Elizabeth, NJ in the 1830s and 1840s. My ancestor is Bridget Denning Flannigan, who emigrated around 1836, lived to be 86 years old, and is buried in St. Mary's of the Assumption Cemetery in Elizabeth. There was also a Thomas Denning who was married to Elizabeth Malone, a William Denning who was married to Mary Baldwin, and a Matthew Denning.
No clue so far as to where in Ireland they came from.