Star Alliance carrier Aegean is offering free flights for up to 8 kids under the age of 12 with 1 paid adult ticket.
This offer is valid for Aegean economy or business class flights booked by May 6 for travel between May 15-August 31.
While the base fare for up to 8 kids will be free, you will still have to pay for some airport taxes.
Unfortunately Aegean does not fly to the US, but they do serve Tel Aviv:
Post what deals you find!