I found a Joseph Carpenter, born in 1793 in Virginia living in Seneca, Monroe County, Ohio in the 1850 census. The 1850 census doesn't give relationships, but it lists with him:
Elizabeth 50 Pennsylvania
Louis 21
Elizabeth 19
Mary 17
Sarah 17
Alexander 11
Except for Elizabeth, all born in Ohio. There is also a John D. Carpenter, 30, in the next household, with:
Louisa 25
George 5
Nancy 4
Vincent 2
Elias 1
Again, all born in Ohio. Next household:
David 30
Catherine 19
Mary E 7/12
All in Ohio. Next household:
Vincent 34
Eleanor 20
Randolph 11
John 10
Elijah 8
Abel 2
All born in Ohio. Next household:
George 33
Jane 27
John 8
Joseph 6
William 1
Maybe Alexander is the youngest you are seeking. I will check the 1860 or 1870 census.
Kathleen