Try searching the Texas Birth Index at this website: https://www.familysearch.org/search/collection/1949342 You might have to create an account with FamilySearch.org, but there is no cost. If the index includes them, you will then know the municipality and date of their births. The Index has the years 1903 to 1997, so if they were born before 1903, try a general search starting from the menu at the top of the screen. FamilySearch.org might even have the full image of their birth records. Good Luck.
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Because you did not give us approximate dates for your great grandparents, I cannot give you a specific answer. This website has a great deal of information about finding Texas vital records Texas Vital Records • FamilySearch