Hello, I'm looking for a Carmain family in Delaware

I have an ancestor named John Carmain. He was born in 1847 in Indiana but in the 1880 census he said that both of his parents were born in Delaware. His mother's name was Mary (b1807) but I do not know her maiden name and I don't know the father's name. I do know that the father died some point before 1850.

I know this is going to be like a needle in a haystack, but does anyone think they can help me?

Thank you!