I own a rental property in NY state. The tenant lost his job, has a family and so I did not want to kick him out at the holidays. I told him he needs to make the home available for showing at all times for new perspective tenants. I tried to give him 24 hours notice today for a showing tomorrow. He said it was inconvenient and he will not let us show the house. I can't afford to keep carrying the home especially if I'm going to have a problem showing to new perspective tenants. I can show where he is closing in on 60 days past due rent. I did not want to evict him and his family but it is becoming apparent I have no choice. What options do I have, do I need to go through the full eviction process if he is 60 days past rent, and if so, how do I start?
Thanks in advance for any help you can provide.

The eviction process generally goes like this:

1) Pay or quit notice: This will be a notice to either bring the rent up to date or vacate. The notice gives 3-10 days depending on local rules.
2) Lease termination: An alternative to the Pay or Quit, this notice terminates the lease for cause and requires at least 30 days notice.

The difference between the two, is that the tenant can pay the rent up to date and cancel the eviction.

If the tenant doesn't vacate by the notice period, then you have to file for an eviction in your local courts. A hearing is held and the judge will grant the eviction. The tenant will have x days to vacate. If they still haven't left you hire a sheriff to physical remove them.