RealClearPolicy's Robert VerBruggen
wondered if births per woman would be greater in countries where more people are married. The short answer is "No." He notes:
Italy, Greece, and Japan -- famously low-fertility countries -- have incredibly high marriage rates.
China is another example of a place with few children (cf. one child policy) but many marriages. Birth and marriage rates are both high in the two Islamic countries shown in his graph: Turkey and Indonesia. Both are also high in India which has a huge Muslim minority.