Below are the relevant statistics.
Next, I will go over my calculation of how much it costs to avert the death of a child under 5 years old ($550) by donating to Lafiya Nigeria.
Contraceptives and other family planning services can avert the deaths of kids under 5 years old indirectly by averting births in sub-Saharan Africa. For each birth that is averted, the child mortality rate is effectively reduced to the average child mortality rate world-wide. Sub-Saharan Africa has a child mortality rate of ~7.4% and the world at large has a child mortality rate of ~3.7%. That means that relocating a birth from sub-Saharan Africa to somewhere else, on average, reduces the child mortality rate by 7.4% - 3.7% = 3.7%.
There are many other benefits of family planning and contraceptive services in sub-Saharan Africa, additionally, but I think the child deaths averted are the largest. For example, if a girl or woman can delay having a child, it can empower her to stay in school longer, improving her work prospects and ability to care for any children she might have later. It also reduces maternal mortality (deaths of women during child birth), both because of the births averted and also because the maternal mortality rate is higher when women and girls give birth at a younger age. So even delaying a birth can prevent deaths of women and girls. And it reduces population growth in sub-Saharan Africa, the region with the lowest income, so that there can be fewer people living with poverty in the future.
To donate to Lafiya Nigeria, you can go here: https://lafiyanigeria.org/donate/
There is a similar charity named MSI Reproductive Choices that also provides family planning services if you would like an alternative. There are a few differences between MSI Reproductive Choices and Lafiya Nigeria.
To donate to MSI Reproductive Choices, you can go here: https://www.msichoices.org/donate/