Kenneth, these are all of the 1860 census records for the name William C. Byrd in Missouri and Arkansas. I included only those with the correct age. This list does not take into consideration any misspellings, such as “Bird.” Hope this helps, and good luck.

o W.C. Byrd, Union TWP, Iron County, MO, age 44, born about 1816 in KY, site under construction – no link.

1860 Census: Union TWP, Iron County, Missouri; Roll: M653_624; Page: 0; Image: 210.

W.C. Byrd, age 44, male, farmer, born in KY;
Margaret E., age 30, female, born in KY;
Alfred M., age 13, male, born in KY;
William C., age 11, male, born in KY;
George W., age 9, male, born in MO;
Jno. A., age 6, male, born in MO;
Martha A., age 5, female, born in MO;
Jackson, age 3, male, born in MO;
Louisa, age 11 months, female, born in MO.

o William Byrd, St Mary’s TWP, Perry County, MO, age 17, born about 1843 in MO, http://home.att.net/~sarankin/119.HTM.

o William Byrd, Pierce TWP, Stone County, MO, age 29, born about 1831 in TN, no link.

1860 Census: Pierce TWP, Stone County, Missouri; Roll: M653_658; Page: 0; Image: 42.

William Byrd, age 29, male, farmer, born in Missouri;
Rachel A., age 28, female, born in Ohio;
William R., age 4, male, born in MO;
John W., age 2, male, born in MO.

o William Byrd, Mill Creek TWP, Izard County, AR, age 32, born about 1838 in KY, no link for 1860

1860 Census: Mill Creek TWP, Izard County, Arkansas; Roll: M653_43; Page: 395; Image: 400.

William Byrd, age 32, Farmer, born KY;
Eliza, age 27, born TN;
Nancy, age 7, born AR;
James, age 5, born AR;
Sarah, age 2, born AR.

(A William C. Byrd does appear on the Izard County 1850 census, age 12, born KY. This link (1850) is http://ftp.rootsweb.com/pub/usgenweb/ar/izard/census/1850/iz1850.txt

o William Byrd, Mulberry TWP, Johnson County, AR, age 48, born about 1812 in AR., no link.

1860 Census: Mulberry TWP, Johnson County, Arkansas; Roll: M653_44; Page: 1022; Image: 529

William Byrd, age 48, male, farmer, born in AR;
Malissa, age 23, female, born in AR.