If you don’t want your kids born here to be citizens, make sure to renounce it formally after each birth.
In the US, you cannot renounce your citizenship if you are physically in the US. A similar situation would seem to agree with regard to Israel. At the Israeli government website dealing with renunciation of citizenship, it specifies that you must be an Israeli citizen *living abroad* to renounce your citizenship. In addition, you will have to present certification from another country that citizenship will be granted. In other words, you cannot deliberately leave yourself (or your child) stateless.
Lastly, the entire process is up to the Interior Minister and can be declined at his/her discretion.
http://www.mfa.gov.il/MFA/About+the+Ministry/Consular_affairs/Renouncing_Israeli_citizenship.htm
The Wolf