Our family has more April birthdays than the next 3 top months combined. 

Not sure what factors could have contributed to that other than random variation, with mostly independent variables like flipping a coin and getting heads 9 times out of 10.

However, on a national scale there are highest birth rate months that do correlate with what was going on at the time of conception.

Why is September the most common birth month?

https://www.givelegacy.com/resources/september-most-common-birth-month/

Ranking the most popular birth months

In the US, more babies are born daily during September than during any other time of year.

According to CDC statistics from 2010, these are the most common birth months: 

• An average of ~11,700 babies were born each day in September
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• An average of ~11,300 babies were born each day in August
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• An average of ~11,100 babies were born each day in July

These are the top 3 months of the year for births. The least popular birth months? Winter months. 

• An average of ~10,800 babies were born each day in February
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• An average of ~10,400 babies were born each day in January 

All but one of the top 10 most common birthdays falls in the month of September.