Dear Scott: I read your E-mail regarding the Dyckmans of Long Island. I will be able to get more info in the future from family members, but I can tell you a few things.
The Dyckmans were well known from the Revolutionary War on Long Island. They had supported the Hessians soldiers, as many Germans on Long Island had during the War for Independence.
The Dyckmans had a dairy farm that supplied much of the Mineola, LI area. One of my family members has a picture from the 1890's of this farm and Rosina Dyckman milking the cows.
My own family is connected through the Mayers and the Krugs, both families of which married into the Dyckmans. The land being rural at this time, the few German families tended to marry into each other.
There are a few Dyckmans buried at St. Boniface cemetery in Elmont, NY. This was one of the old German cemeteries of the area. They may have records that could help you further. Thanks again!