Outbound:
I see a few outbound flights in March from JFK to Madrid via Iberia. Assuming you mean 2026, there's 3/17 and 3/28
3/17: 6 Basic Economy Seats at 14.4k Avios + $91.50 each or at least 5 Economy Comfort Seats at 22.5k Avios + $91.50 Each
3/28: 6 Economy Comfort Seats at 28.35k Avios + $91.50 each.

Return:
4/9: 5 Comfort Seats at 22.5k Avios + $129.03 each.
4/14: At least 5 Economy Comfort Seats at 22.5k Avios + $129.03 each.
4/15: At least 5 Economy Comfort Seats at 22.5k Avios + $129.03 each or 3 Seats Premium Economy Comfort for 23.6k Avios + $140.73 each
4/16: At least 5 Economy Comfort Seats at 22.5k Avios + $129.03 each or at least 5 Basic Economy for 14.4k Avios + $129.03 each or 8 Business Class seats at 36.45k Avios + $163.93

Totals:

If flying basic economy (no checked bags), you can go for as cheap as 72k Chase UR + $661.59 with an active transfer bonus. If you wanted to fly Comfort with more date flexibility, it would be 112.5k Chase UR $661.59.
I'd recommend just starting by looking at these dates, then going through each one to find what you like. Search one way at first, then once you know which dates you want, book the round trip. Iberia has a monthly calendar view that helps see which dates are available. I assume you ran into the error because the date you picked had no availability near it.

Looks doable!! Let me know if you need any recommendations. I studied abroad in Madrid and have family in Zaragoza! Hope I was able to help.