Hi Dolly, I guess I shouldn't be surprised threre is no birth information prior to 1900 or so. I guess I would have thought also that New York (Eastern states being so settled) their requirements would be greater then the midwest states as being admitted to the union so much later. Its the marriage certificate that should have turned up, as even in WI they are available for the years in the 1840's. I can only think he married under a name that is spelled somewhat different then the name you gave them, and they are not inclined to look further. Often times that information is in their archives and whether it is microfilmed. I would think the LDS would be able to locate a microfilm for you to review. It would be a help if you could come up with a religious affiliation as it may have been a church wedding and info could be buried in some church records. Do you have any particular place in New York or is it the city of New York. I gather you do or do- not have the maiden name of that "first wife"? As you say a divorce. I know that death records don't always have the parents,it depends alot on who the informant was and what they knew. I don't think finding him in a cemetary is going to be of any help, as you do have a death record. Its the marriage certificate that needs to be concentrated on as I've never seen one that doesn't ask for parents names. I would also be searching through the familysearch.com and with hope he'll show up in some microfilm. Was he an age where he could have served in the civil war ., (the records would show if he had applied for a pension, or his wife had). If nothing else it has his age, & his description.
I'm not certain this can't be solved without parents names. Its just going to take a whole bunch more digging. One thing good about the Eastern States are all the genealogy societies, history that has been published through the years and the literature/periodicals they published. I hope you have or are considering ordering marriage certificates of his children, you may come across different spellings of the name. May I also suggest the purchase of another book,its really chuck full of great information .
"They Became Americans"(finding Naturalization Records and Ethnic Origins). by Loretto Dennis Szucs. It runs around 19.95 , Ancestry sells it & Likely in any large book store.
Good Luck and its just going to take awhile yet. You are bound to find the information you need eventually,
Jane