by 5.2 years, on average! Quite a strong effect and many of the results are statistically significant (p less than 0.05), according to a Norwegian study  that analyzed 202 years of data over a population of 8662 people. See also this article.
A Solar cycle takes 11 years on average, thus the period of the study (1676-1878) spans about 18 cycles. Interestingly, intensity of cosmic radiation goes down during solar maximum, due to the shielding effect of the active solar wind against Galactic cosmic rays. Could the lower level of ionizing radiation background present during Solar Maxima  have had a detrimental effect, and the higher level during the Solar Minima - may have had a beneficial effect on the newborn babies? This is my purely speculative interpretation of course - but see my other articles on ionizing radiation!
Results are shown in the Figures 1,2 and 3, from the referenced paper:
1. "Solar activity at birth predicted infant survival and women's fertility in historical Norway",
Gine Roll Skjærvø, Frode Fossøy, Eivin Røskaft,
DOI: 10.1098/rspb.2014.2032, Proceedings B of The Royal Society, Published 7 January 2015
2. Cosmic radiation background is strongly and inversely dependent on the Solar activity. Cosmic radiation is the highest and the Sun is the least active, the Sunspot number is the lowest at Solar Minimum, for example, see the following graph:
The effect is stronger at high latitudes, like in Norway, where the magnetospheric shielding is lower. Incidentally higher level of Cosmic Radiation during low Solar activity results in high global cloud cover due to cloud seeding, which in turn lowers the global temperature. This is a stronger effect than due to CO2 variation, according to some studies [to be quoted].