I looked further, and found that charities that openly support this strangely controversial form of aid are few and far between. It seems that except for an organization explicitly dedicated to reproductive rights, supporting the right of women to control their reproduction is too risky - it might alienate Catholic, Evangelical, and other conservative donors.
Education and opportunity are the route out of poverty, but I think that supporting reproductive choice in the developing world can make a much bigger difference than directly supporting education, especially in countries where a reasonable level of education is already available. If couples in the developing world can limit the size of their families, education and opportunity should follow, even without our help.
With a baby arriving every 12-24 months, many parents are unable to earn enough to support their children. The older kids may have to work to support their younger siblings, taking time away from education, or preventing it altogether. Schooling is unaffordable with that many mouths to feed, or only affordable for the boys. The mother's near-constant pregnancy and time spent caring for an infant and young children will impact her ability to provide for her family, assuming that she survives at all. Worldwide, 800 women a day die from pregnancy-related complications.1 Of women in the developing world who reach survive to the age of 15, 1 in 150 will die of maternal causes,1 and twenty times that number will suffer serious, sometimes life-long complications.2 Of course, those numbers were for the developing world as a whole, where 50% of women still have access to contraceptives. In sub-Saharan Africa, 1 in 31 women will die from pregnancy and childbirth complications, and in Afghanistan, the figure is a shocking 1 out of 7.3 Motherless children are 10 times more likely to die within two years of their mother's death than children whose mothers are still alive.4 Overall, the picture is grim.
It doesn't have to be this way. Consider a hypothetical family in the developing world. They are poor, but have access to family planning services. They don't start having children as soon as they marry, but hold off for a few years, and are able to scrape together some meagre savings. They have two or three children, comfortably and safely spaced, and then stop. Mum and Dad's work between them provide enough income to feed, clothe and educate their children. The children don't need to work, or don't need to work as much, so they can focus on education and thus have a chance of breaking out of the poverty cycle. Not only are fewer children being born into poverty, but those who are born are much less likely to live in poverty.
Unfortunately, as I alluded to earlier, charities operating in this field are few and far between. I personally give to Marie Stopes International Australia (MSIA), who provide sexual and reproductive healthcare services around the world. This includes providing contraception, sexual health education (including on STD prevention), mother and baby care, and yes, safe abortions in countries where abortions are legal. MSIA was the only reproduction targeted charity I could find based (and therefore tax deductible) in Australia. However, in this case, a choice of one isn't a problem for me, because they appear well run, and I support their goals. For non-Australians, Marie Stopes International has divisions in a number of different countries, or you could consider DKT International or the International Planned Parenthood Federation. If you know of other organizations, please share in the comments. Also feel free to comment on how you see the relative importance of this compared to other aid needs in the developing world.