Tenant wants to stay after lease expiration

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I gave my tenant oral notice yesterday (April 12) that I need the apartment after his lease (expires July 1) is up. So it is basically a 78 day notice. Tenant basically replies with I should have told him sooner and that he wants to at least live until the summer is almost over. He said he wants to enjoy the summer instead of wasting it on moving and looking for a new place to live. He said he will start looking around Labor Day (beginning of Sept). My wife and I agreed to let him live and start looking in Sept. The property is located in Nassau Country, Long Island, New York. This July 1st will make 1 year tenant has lived in unit. Tenant has never been late on rent thus far. I am trying to avoid court as much as possible unless he stops paying rent or stays excessively too long in unit.

My question is should I give him a new short term lease or no lease?

Thanks in advance.