Dear Ms. Ballard,
Thank you for posting your request on History Hub!
The Federal Government does not ordinarily create or maintain birth, death, marriage or divorce records. Such records are made and kept by State and local governments rather than the National Archives. We suggest that you search the FamilySearch index to Maryland Births and Christenings, 1650-1995, and request a record search from the Maryland State Archives (obtaining the certificate for births less than 100 years old is restricted). In addition, the FamilySearch Research wiki for How to Find Maryland Birth Records may be helpful.
We hope this is helpful. Best of luck with your family research!
According to the Maryland State Archives, birth records must be 100 years or older to be accessed. They do have an index (in PDF format) that you can search.
The page above states that the birth certificates are arranged in chronological order by month, then alphabetical order by county and surname.
Choose the year range you wish to look at from the list, and then the letter of the last name. Click on the corresponding link. Jump pages until you get to the page with the last name you want. Once there, you will need to go through all the entries to see if the one you wish is there.
This is assuming that the child was born in Maryland and not in another state.
Welcome to History Hub
Your post is a little confusing is Corrine the child you speak of or the mother of the child. Who was the father of her two sons Leroy and Willie? Did Corrine ever use the name Cora?
Corrine was 7 months old at the time of the 1920 Census, that would make her 16 when/if she died in 1936.