I was able to get total fertility rate (TFR) estimates from the CIA World Factbook. I subtracted 2.1 from each score--the rate necessary to keep a country's population stable. Positive scores reflect the extent to which a society is growing. Negative scores show the degree to which a society is dying.
I correlated this measure with the percent of the population that attends church weekly (World Values Survey). For 91 countries, it is .68--a very strong relationship. Societies with low numbers of people going to church are very likely to be dying.
By the way, I noticed that few countries are really close to 2.1. Societies tend to be either growing or dying.