There are much easier ways to fix this:

Option 1) You could make it easier to afford and raise children.

I realize this seems a little extreme in a US context, so here is a more affordable option:

Option 2) You could encourage women to get an abortion if they're pregnant with a boy.

All we need to maintain the population is that each woman on average produces one new woman. Plus a few men, perhaps acting as sperm donors.

I jest, of course, but my point is that there's more than one way to be authoritarian.