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An interesting question!

I did not see mention of Rikers Island in the Van der Donck book, however "A Brief History of the Riker Family: from their first emigration to this country in the year 1638, to the present time” (http://catalog.nypl.org/record=b13703276~S1) notes that Abraham Rycken obtained the island in 1664.

You will find several mentions of Abraham, or Abram, Rycken in the “Records of New Amsterdam from 1653 to 1674” (http://catalog.nypl.org/record=b10395000~S1).

Finally, "The Other Islands of New York City" (http://catalog.nypl.org/record=b12623667~S1) has a longer chapter on the history of the island, differing somewhat on the details from the first title above. This source asserts that the land was purchased from unnamed Native Americans by Sheriff William Hallett in 1664. The purchase was not officially sanctioned and therefore overturned by Peter Stuyvesant, who then gave the island over to Abraham Rycken at a later date.

"Other Islands" also states that the Riker family sold their island to the city in 1884, for the sum of $180,000.