First, look at South Korea. They have the worst birthrate (not fertility) problem. Over the past 80 years, they created a culture focused on work with no work-life balance. Employees are expected to get drunk with their boss after work, rather than go out looking for a date or go home to their family. While they now offer things like paternity leave, if you take it, you lose the chance to get promoted. Which leaves you too poor to raise a child.
Next, our culture has allowed the costs of raising a kid to rise to about 1/2 million us dollars or about 8 times the average US income. This encourages women to make their number one consideration how much money a guy makes. If you see a beautiful woman with an unattractive guy you think he is rich.
There are a lot of factors involved in this issue, including the importance and expense of school (both lower grades and university), and the obsession with spending money on expensive things to get into the right college (after school activities). In the 1950s your average yearly college cost of a GOOD school was half the average salary, Now it approaches double it.
If we really want to encourage people to have children, no amount of tax discounts will do. You can't remove a mountain with a shovel, you need excavating machines.
We could put high taxes on any university that has more than half of their students paying more than half the US average salary. This would focus more of the money on education rather than research, which does have consequences.
We would also have to require them to separate out any activity that cost any money to do in their admissions applications and make it only apply to people paying full cost. That would specifically include people attending private high schools. If you can afford to go to them, you have to pay full price college admissions - and only compete against others.
This would punish certain states that are trying to save public money by encouraging parents to put their kids in private schools. NO. Do not make it more expensive to raise kids in order to save taxes for the wealthy in your state.
Then there is food and healthcare. They should be near free to all children under the age of 18. Every school should offer free lunches to all students - and require them to be both healthy and delicious. This is NOT hard to do, other countries do it all the time. Sweden, Brazil, India are fine examples. The trick is to have a separate budget, so nobody cuts the food budget because they cut the education budget.
Health care again should not depend upon how much money your parents made, we cover the healthcare of the elderly, just put all kids in Medicare until age 18.
Will this cost money? Yes. but it solves the problem we created by trying to save money in the wrong areas.