I have found that the DHS Program (US AID) and UNICEF's Multiple Indicator Cluster Surveys are great resources for obtaining birth and socioeconomic data. US AID surveys contain a whole wealth of data on maternal and child health and cover a lot of western Africa. Unfortunately, due to the recent Ebola outbreak there haven't been many surveys performed in West Africa in the last year or so, but there's a great backlog to monitor temporal change in birth rates.

Both of the sources require registration (links to each website below), but are free to access.

http://www.dhsprogram.com/

http://mics.unicef.org/

Alternatives to these sites include visiting the country-specific national statistics websites and investigating what survey's they've performed and applying for access that way. A few to get you started:

Cote d'Ivoire - http://www.ins.ci/n/

Liberia - http://www.lisgis.net/

Sierra Leone - http://www.statistics.sl/

Please do let me know if you have any questions regarding the DHS Program/UNICEF MICS sources; I have experience using their data-sets. 

Go to:

Google Scholar and Pubmed

Type:

Pregnancy in West Africa from 2013 to date