You can contact Van Buren County here for a birth certificate - there is a fee involvedhttp://www.vbco.org/government0149.asp
I can see your confusion - the 1900 census, has her birth September 1899, the social security death index says 1896 and the Michigan death index says 1898. Normally, I would say that the SSDI is more accurate, as the person themselves reports the information, as opposed to the death certificate. However, I would lean more toward 1898 as that is a closer match to her age in census records. The other thing to consider is that the Michigan death index and social security death indexes online are both transcribed/entered by humans, which on occasion are known to misread things! You can request a copy of her social security card application, but due to some states privacy laws, you may not get complete information as you used to.