A. There might be award availability even if Continental.com doesn't have it. For example, Swiss Air flights are not listed online, but can be booked with OnePass miles. Call to check for availability.
To call CO without waiting on hold use this link:
http://bit.ly/oGou3M.
B. Award availability between TLV & NYC will not open up a day before the flights leave. As a rule airline award availability is set months in advance. Even if that wasn't true, flights between Israel and NY are usually at max load, certainly in late August. You will have trouble finding regular Economy seats, never mind reward.
C. If you plan on going to Israel again within 12 months, you can book end-on-end. Instead of making the return half of your reward ticket now, make it for the your second return from Israel (next time you go), then book a round-trip from Israel to NY, departing Israel when you want to return from your first trip, 'return' from NY to TLV when you want to leave on your second trip.