My mother's maiden name was Tackbary. We traced her ancestry and it went back to a Henry Tackbary who was born in Ireland in 1824. We don't know anything about his father, but his oldest son was named William.
He came to the USA around 1850 and by 1860 had settled in upstate New York, with his wife, Bridget Jane.
This really sounds like a possible fit! Could you please e-mail me if you get this message?