Gerhard Friedrich Bünger Emmigration

I would like to know the port of entry to the U. S. and departure port
from Germany and the Ship name for the following family:

Gerhard Friedrich Bünger (born 1836), his wife Sophie Louise Wilhelmine
(geb. Wulf, born 1836), and their children Sophie Charlotte, born 1856;
Friedrich Heinrich born 1858; Frederick Heinrich Rudolph, born 1860; and
Heinrich Ludwig Georg born 1864.
They emmigrated from Germany sometime between February 1864 and March 1865.

I have searched all of the immigration records that are available to me in
the U.S. and have not found this family. Are there any records available
in Germany that would give me the emmigration information for this family?

Thank-you

Janis Bunger-Clausen