Are you sure your facts are correct? The 1850 census for Iowa says Joseph was born in New Jersey not New York. And, was he married in Pike County, Ohio? Or is it Lake County, Ohio? Or is it Pike Township, Brown County, Ohio? There is no "Like" Ohio.
I know I sound picky but location is everything in genealogy especially when you're dealing with a name as common as Joseph Brown. There are millions of Joseph Browns to sort through.