Maintaining stable population levels is actually a LOT harder than you think and there are a range of issues you have to face. First of all, not everyone wants children. Secondly, you need to cater for accidents, murders, and other unforeseen circumstances (not to mention emergent homosexuality) in your world.
Then, there's age distribution. You ideally want as large a (stable) percentage of your population in working age if at all possible. Otherwise, you end up with ageing population issues which mean that a lot of your resources are being tied up with caring for the elderly and not producing food, clothes, housing, etc.
I remember reading that in the Renaissance, the number of children per family to maintain population numbers in Europe was around 4. This was because many couples didn't have or want children, and some people were bachelors or spinsters all their lives.
If you look at China and their 1 child policy, that has led to a runaway ageing population problem that is going to be at its most severe around 2050.
But wait (I hear you say), we have around 2.1 kids per family NOW and we're facing overpopulation, aren't we?
Well, no. Since most developed countries have embraced females into the workforce, our economies have effectively doubled since the 1970s but at the price of population replacement. Most developed countries now ONLY have population growth thanks to immigration. Australia, Germany, Japan, and many others are facing ageing population issues which (while not on the scale of China) are going to cause headaches in the next 50 years. Ironically, the only countries that are contributing to global population crises are those who have a far less enlightened view of the role of women in their societies.
Ultimately, if you want your population to be constant, you probably want at least some women in your group dedicated to having and rearing children. That doesn't mean treating them as less than equal; it means making the raising of children a 'career' that is valued every bit as much as hunting, gathering, etc. in your community. If you value the raising of children, then more children will be born to your community and it's only if the numbers climb beyond the percentage allowed for pre-working age population numbers that you need to put a temporary stay on new births, until more are of working age.
Depending on the other careers available, if only around half your women actually want to have kids, then the magic number is around 4 kids per woman. If more want to have kids, then the ratio goes down. You're best working this out as a percentage of families, rather than a percentage of kids per population.