in January 1806
Yes, Coney Island was once an island. Now it is a peninsula.
It was only separated from the rest of Long Island by a narrow creek, called Coney Island Creek. The center of the creek (the part that separated Coney Island from mainland Long Island) was filled in sometime in the early 20th century, turning Coney Island into a peninsula.
This is the plot of the 1959 film Imitation of Life, directed by Douglas Sirk.