Church/parish records in the US are not anywhere as likely as those in the UK to provide the kind of information you are after. This is because there was no requirement for registering births until relatively late in US history. After 20 years of research on my scores of US ancestors I can count the number of church records I have found on one hand with digits left over.
Unless you already know what (if any) church your relative belonged to, and can contact them, and they actually have retained the records in an archive, you are probably wasting your time in pursuing this avenue of research.
Sad to say, but true.
Nick