Dates of birth and death are from his gravestone, as recorded on FindAGrave.com.

Her death certificate, scanned online at the Missouri State Archives, lists Eliza Emeline Downing, widowed, age 83 years 1 month, born 5 Feb 1842 in Illinois, died 5 Mar 1925 in Warrensburg, Johnson Co., Missouri, father Thomas Burkett, his place of birth unknown, maiden name of mother unknown, cause of death bronchial pneumonia, informant Mrs. J. J. Davis, Warrensburg, Mo, burial in Hobson Cemetery.

Mrs. J. J. Davis is her daughter Gertrude.

I cannot find any match for her in the 1850 or 1860 censuses, under either Burkett or Harris, unless she is the Emma E. Burkett who was a daughter of Needham Burkett and his first wife Annis Pruitt:

1850 census of Fayette Co., Illinois, enumerated 12 Sep, lists as family #488:
Needham Burkett, 39, b. N.C.; Julia F., 27, b. Va; Elizabeth M., 20, b. Tenn; William, 18, b. Tenn; Andrew, 14; Martha, 12; Dolly, 10; Mark, 9; Emma E., 7; Annis, 5; Thomas, 3; Francis W. (m), 1. Andrew through Francis born in Illinois. The gender for Francis does not match the 1860 census.

Fayette Co., Illinois marriage records list the marriage on 16 Apr 1846 of Needham Burkett and Julia Franklin Pryor, so only the two youngest are her children. The others are children of Annis Pruitt or Pruett, whom he married in Tennessee about 1830.

1860 census of Newton Co., Missouri, Van Buren township, enumerated 14 Aug, lists on p. 175 as family #1179/1206:
Needham Burket, 52, farmer, b. N.C.; Julia, 39, b. Va; Thomas, 14; Frances (f), 12; Needham, 9; Jane, 7; Arena, 5; Lear (f), 3; Rosey, 2, b. Mo; Ellis, 11/12, b. Mo. Thomas through Lear born in Illinois.

Missouri marrage books scanned online at Ancestry.com record the marriage on 7 May 1868 of Mr. John Downing to Emiline A. Harris both of Johnson Co.

1870 census of Lafayette Co., Missouri, Freedom township, enumerated 1 July, lists on p. 55 as family #353/360:
Downing, John P., 43, b. Ky; Elisa, 25, b. Illinois; Thomas, 11, b. Ky; Jesse M., 8, b. Indiana; Harris, John, 10, b. Missouri; James, 7, b. Missouri; Downing, George, 1, b. Missouri.

The preceding household is John’s oldest son, James F. Downing age 23, and his wife Martha. The one before that is Manoah and Virginia Dyer, whose daughter Ann America was married to William Washington Downing, son of John’s brother James F. Downing. (W.W. and Ann were in Davis township.)

1880 census of Johnson Co., Missouri, Hazle Hill township, enumerated 9 June, lists on p. 10 as family #77:
Downing, John, 52, farmer, b. Ky Ky Ky; Eliza, 38, wife, b. Ill Tenn Alabama; Jessie M., 18, son, b. Ind Ky Ky; Eddie, son, 11; Elba P., son, 9; Gertie L, dau, 6; Emmet E., son, 4; Anna, dau, 2; Harris, James P., 18, stepson. Eddie through James all listed as born Mo Ky Ill.

1900 census of Johnson Co., Missouri, Hazel Hill township, enumerated 23 June, lists on p. 11B as family #226:
Downing, Eliza, 58, b. Feb 1842, Illinois Illinois Illinois, widowed; Emmett E., son, 23, b. Mar 1877, Missouri Indiana Illinois; Curtis L., son, 12, b. Missouri Indiana Illinois; Archer, Samuel E., son-in-law, 28, b. June 1871, Missouri Missouri Missouri; Uula M., dau, 18, b. June 1881 Missouri Indiana Illinois, married 0 years, 0 children; Lemmon, John, boarder, 72, b. July 1828 Ohio Scotland Scotland.

(Although John was really born in Montgomery Co., Ky, the Dennis Downing family moved to Henry Co., Indiana when he was only 1 year old.)

1910 census of Johnson Co., Missouri, Hazel Hill township, enumerated 2 May, lists on p. 8B as family #164/167:
Downing, Curtis L., 21, b. Mo Ky Illinois, farm laborer; Eliza E., mother, 68, widowed, b. Illinois Alabama --, mother of 8 children, 7 living.

1920 census of Johnson Co., Missouri, Hazel Hill township, enumerated 6 Jan, lists on p. 2B as family #46:
Downing, Eliza, 77, widowed, b. Illinois Tenn Tenn; Lee, son, 31, single, b. Mo Ky Ill, farm laborer.