Joenna, I have absolutely not found anything but straws ... but assuming you're almost at the straw-grasping point... First straw... assuming that "Nettie" might be short for Annette or Antoinette, and (more straws) that she may have begun using her middle name when she got older... Maybe she's Sarah A. Baysinger, age 8 below, which would have her born about 1872. (I included the rest of the family from the 1880 US census. At least they're from Indiana....
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/3:1:33S7-9YBC-C3K?cc=1417683&wc=QZ2W-SJH%3A1589401272%2C1589394993%2C1589397727%2C1589394803 : 24 December 2015), Indiana > Crawford > Sterling > ED 29 > image 27 of 42; citing NARA microfilm publication T9 (Washington, D.C.: National Archives and Records Administration, n.d.).
Nicholas D Baysinger Self M 36 Indiana, United States
Elza A Baysinger Wife F 37 Indiana, United States
Elizabeth J Longest Stepdaughter F 16 Indiana, United States
James D Baysinger Son M 14 Indiana, United States
Sarah A Baysinger Daughter F 8 Indiana, United States
Samuel R N Baysinger Son M 6 Indiana, United States
John M W Baysinger Son M 4 Indiana, United States
David S T Baysinger Son M 1 Indiana, United States
There are also some Indiana-based Baysinger Wikitree profiles from around the right time (but without the right names...) Baysinger 85 through Baysinger-91 are all Indiana based Baysingers, but with very few additional helpful details....The profile manager may still be active, and perhaps he or she can provide additional clues.
One final straw ... Is it possible that Nettie Baysinger was her name from a previous marriage, and then the widow married again to Hezekiah Cooper? Maybe that's why she's hard to find.
Oh, there WAS one Findagrave Nettie A. Cooper in Indiana, b. January 25, 1874 -- But it really doesn't look too promising. You can check it out at https://old.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=143278887
I wish I could have actually found something helpful. At least I stopped hitting my head against my own brick walls for a while...YOUR brick wall seemed softer, since I knew I could stop when I wanted to....;-)
Reba