You'd have to go online to the State of Tennessee, Department of Vital Statistics. There you can order birth, marriage and death records. You have to show a relationship to get a birth record, so I used a copy of my drivers license and explained my relationship the last time I ordered one. They were $12 then. You might also get his obit if you contact the Dresden Enterprise Newspaper and request it.
If you don't know the county of birth for sure, they should be able to find it by birth date. I know the surname will be an issue, but the first name Hargis is a standout. The family lived in Jackson County, TN in 1930, but Mr. Cherry's grandfather, E. Wooten Cherry died in Weakley County, TN in 1938, so Hargis may have been born in either county. I think the more you can tell them, the liklier they will be to find the record. It's been quite a while since I did this myself, so if anyone reading this has better information, please pass it along.