It sounds like you are asking about circulating coinage in Colonial NY .
Below is a paragraph that will give you an idea of what was around in 1711.
Thanks to UND for what I consider the best online info regarding Colonial Coinage:
Colonial Coins - Section Contents
"An estimate of the quantities of coinage circulating in the New York colony can be gleaned from the remains of the English 32 gun frigate H.M.S. Feversham. While in New York City it was recorded on September 4, 1711, that the Feversham was given £569 12s5d from the British treasury office in New York. it represented the coins then in circulation in New York City. On September 17, 1711 the Feversham set sail for Quebec. On Sunday October 7, 1711, during their journey north, the Feversham sank on the rocks off the shore of Scatari Island near the coast of Nova Scotia. In 1984 the Feversham was found by a private group that conducted salvage operations over the next few years. Among the items found on board were £33 13s in coins, presumably a portion of the allocation that had been obtained in New York City. This hoard contained 8 English silver coins, 22 Dutch coins (Lion dollars), 5 coins from Spain, 504 New World Spanish coins (from one half to 8 reales coins) and 126 pieces of Massachusetts silver. the Massachusetts silver consisted of: one NE shilling, being a Noe 3-C; four Willow Tree shillings, consisting of a Noe 1-A, 3-D, 3-E and one example too worn to classify; thirty five Oak Tree shillings; one Oak Tree sixpence; seventy five Pine Tree Shillings and one Pine Tree sixpence as well as nine cut pieces that had probably been used as small change, consisting of four half shilling pieces and five quarter shilling pieces. From the Feversham find it appears that proportionally, Massachusetts silver was second only to Spanish American coinage in New York."