Peter is my great grandfather. His daughter, Louisa was my grandmother. I have documents that say Peter was born in Hunterdon Co., NJ. Several Census records show Peter reporting that both of his parents were born in NJ. I suppose he might have been varnishing the truth, but I will go on the assumption that his parents were born in NJ.
His son Fred gave the info on the death certificate and may not have had access to correct information. I have not been able to find any record to support that Peter's father was named Martin.