Maura,
The best I can determine from the 1850 Ohio Census, is that Matthew and Mary Cullen were married somewhere in Ireland as their first child, John, age 3, was listed as being born in Ireland. Their second child, Ellen, age 1, was listed as being born in Connecticut, U.S.
Also, from the 1850 Ohio Census, there is a James Cullen, living beside the Cullen and Doyle family. James was listed as 38 years old and married to Rosannah (from Pennsylvania, U.S.) with the following children: Peter - age 8, Mary Ann - 6, Harriett - 4, and Samuel - 2.
James (born about 1812 from Ireland) was close in age to Matthew (born about 1815), so I would think they are either brothers or cousins.
Jackie