I'm afraid you'll find that Birth Certificates were as rare as the proverbial hen's teeth here in the U.S. anytime prior to ca. 1910 or so, and then only in selected areas. One thing you could do through Ancestry or even sites like this:
http://www.censusfinder.com/
is to check the Texas 1900 Census. Unfortunately, the census (every 10 years here) for 1890 was mostly lost to a fire in Washington D.C.
The census search is aided greatly if you happen to know the County in Texas in which your search is located.
Secondly, although birth certificates are rare, most States have reasonably good marriage certificate records. Again, if you could know the County, they often have genealogical societies that post on line, such as this:
http://usgenweb.org/
Best of luck!