How can I get a non refundable deposit back from my wedding venue in NY?

You can request anythng, but the venue may not honor your request.  Frankly, given the current situation, the venue may not be able to afford a refund.  Assuming that you can't reach agreement with the venue, you could sue to seek to rescind your agreement, arguing that the covid pandemic has frustrated the central purpose of the agreement and/or has made the contract impossible to perform.  Before you do so, however, you should review the contract to see if it contains a "hell or high water" or "force majeure" provision which would provide something along the lines that the risk of any event occurring which prevents the wedding from taking place is on you.