My name is Joe Leyden from Kilkee, Co. Clare, Ireland.
I have just seen your posting of Nov 2010 and would like to help you if I can. I am all too familiar with genealogical "brick walls" particularly when trying to trace my family.
My branch of the Leydens is from Kilfenora, Co. Clare, Ireland, and that county is where I would start your search from scratch. They were many Leydens in that county over the years and looking there is your best bet at the moment.
If that draws a blank, I will direct you to other Irish counties with Leydens such as Galway, Roscommon, Sligo & Leitrim. There are several ways to spell the Leyden surname but mine is spelt the same as yours.
Do you know the names of any of Peter's brothers & sisters as I may be able to find them or their descendants in the Irish 1901 & 1911 census?
Did Peter apply for US citizenship as, if so, his naturalisation application may have personal details about where he came from?
Did he live anywhere else in the US apart from Hoboken NJ?
Send me an email if you would like me to try & help.