There are no RELIABLE very “cheap” tickets.
Best tips are to avoid peak travel times, i.e. Jewish or goyish holidays, to avoid weekend travel, and in general to try to be flexible with dates.
The online travel websites like Orbitz, Expedia, and Travelocity (that are the best for domestic fares)are generally NOT as good for travel to Israel as a Jewish travel agency that specializes in Israel and knows when and where to get the best rates.