Flights are available on both American and Delta at this price point, but dates are a bit harder to pin down. Availability is fairly sparse in certain months, but it is out there! Your best bet is to try and book two separate one-way tickets at $51 a piece and stitch together a custom itinerary of your own.
As an example, searching on AA.com, I found weekend travel departing MIA on Friday, January 25 and returning from LGA on Monday, January 28, 2019. Dates in January and February seem to have more seats widely available.
Need a room in NYC? Here's a list of available accommodations for the listed dates on Hotelwatchdog.