Fertility rates in Israel are interesting not just for their relevance to Middle Eastern affairs, but for their relevance to America. Not surprisingly, the Israelis pay close attention to such matters, but Americans traditionally don't pay attention to Israeli population policy debates for the insights they can offer into American population policy. So, it takes some looking for Americans to find Israeli data.
Thanks to commenter Douglas Knight, here's a graph from Israel: Demography 2012-2030: On the Way to a Religious State by Bystrov and Soffer. This shows total fertility rates (expected babies per lifetime) from 1980 to 2008 for different classes of Jewish Israeli women. The top line is Ultra-Orthodox, who were down to 6.6 from a high of around 7.7.
At the bottom are Secular at around 2.05, which is the replacement rate. That's a pretty high TFR for secular women in a crowded, advanced country. (Israel's not that different in terms of climate, terrain, population density, and real estate prices from Southern California.) How does Israel achieve replacement level fertility among its least likely category?