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This is weird. I found a 1900 census with the exact names and dates of birth for Bill and Sarah but lists Cora and Bulor's birthdates different from what you have suggested. The link below is from familysearch.org. I also attached the 1910 census which lists the same people and also some Kelley's. In this census, the names are misspelled and the birthplaces for Bill and Sarah are different than what you suggested. I hope this helps and doesn't muddy the issue. I have found in my own search that occasionally names were written incorrectly by census takers. If you have Bulor and Cora's birthdates confirmed these may not be helpful.
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Dear Ms. Wolfram,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Population Schedules for the 1900 Census and the Population Schedules for the 1910 Census in the Records of the Bureau of the Census (Record Group 29). Unfortunately, digital images for Pike County, Arkansas have not been added to the Catalog yet.
Therefore, we searched the 1900 Census on Ancestry and located a Bulor Barnett (4) and a Cora Barnett (8) who were daughters of Bill Barnett and his wife, Sarah, and lived in Pike County, Arkansas. We also search the 1910 Census on Ancestry and located a Bula Barnet (14) who was the daughter of William and Sallie Barnet and lived in Pike County, Arkansas. To view these records, there may be a fee. Or you may view these records online at one NARA's facilities for free via ALIC. For the nearest NARA location, please consult our web page at https://www.archives.gov/locations/. Also, some of the images from Ancestry are available for free on Family Search at https://www.familysearch.org/en/.
For more information, please contact the Arkansas State Archives for vital records such as birth, death, and marriage records. Please check the county records as well.
We hope this information is helpful. Best of luck with your family research!
I found those on familysearch.org. You need an account but it is free. See my post below.