Everything seems to indicate that he did not use a middle initial.

There are 12 John Cunningham's listed but I don't know where they enlisted. Perhaps someone else can reduce the numbers even further.

John Cunningham 2nd Regiment, Tennessee Cavalry (Smith's) Confederate
John Cunningham 4th Regiment, Tennessee Cavalry (McLemore's) Confederate
These two could be the same man - 2nd (Smith's) Cavalry Regiment [also called 10th or 11th Battalion] was organized in February, 1862, with eight companies. During April its numbers had increased to regimental strength. The unit served in the Department of East Tennessee, but was soon mustered out of service. Two companies were transferred to the 4th (Starnes') Tennessee Cavalry Regiment and some of the men joined Alabama commands. Colonel E. S. Smith and Lieutenant Colonel Zachariah Thomason were in command.

John Cunningham 10th Regiment, Tennessee Infantry Confederate
John Cunningham 8th Regiment, Tennessee Infantry Confederate

John Cunningham 18th Regiment, Tennessee Cavalry (Newsom's) Confederate
John Cunningham 19th/20th Consolidated Regiment, Tennessee Cavalry Confederate
These two may be the same man as the 18th also consolidated with the 20th

John Cunningham 22nd Battalion, Tennessee Infantry (Murray's) Confederate This unit merged with the 38th Regt, TN Inf in1863

John Cunningham 23rd Regiment, Tennessee Infantry (Martin's) Confederate

John Cunningham 21st Regiment, Tennessee Infantry Confederate

John Cunningham 22nd Regiment, Tennessee Cavalry (Barteau's) Confederate

All of these units were badly beaten up by 1865.

John Cunningham 10th Regiment, Tennessee Cavalry Union

Cunningham, John 11th Regiment, Tennessee Cavalry Union

1870 United States Federal Census
Name: Mordicia Cunningham
Estimated birth year: abt 1858
Age in 1870: 12
Birthplace: Tennessee
Home in 1870: District 6, Claiborne, Tennessee
Family and neighbors: View Results
Race: White
Gender: Male
Value of real estate: View image
Post Office: Tazewell

John Cunningham, W/M 40 Father/Head of Household/Farmer b. TN
Silvenia Cunningham W/F 41 Keeping House b. VA
Hezekiah Cunningham W/M 13 Working Farm b. TN
Mordicia Cunningham W/M 12 B. TN

Tennessee Marriages, 1851-1900
Name: JOHN CUNNINGHAM
Spouse: SILVENA BURCHET
Marriage Date: 30 Aug 1855
County: Claiborne
State: TN

1880 United States Federal Census
Name: John Cunningham
Home in 1880: District 6, Claiborne, Tennessee
Age: 49
Estimated birth year: abt 1831
Birthplace: Tennessee
Relation to head-of-household: Self (Head)
Spouse's name: Sylvinia
Father's birthplace: Tennessee
Mother's birthplace: Tennessee
Neighbors: View others on page
Occupation: Farmer
Marital Status: Married
Race: White
Gender: Male
Household Members: Name Age
John Cunningham 49 W/M Farmer
Sylvinia Cunningham 51 W/F wife Keeping House
William F. Cunningham 14 W/M son at home
Calvin Cunningham 12 W/M son at home
Martha Cunningham 7 W/F daughter at home
Marry Cunningham 7 W/F daughter at home

Next door lives:
Mordicia Cunningham 22 W/M Farm laborer
Mary A. Cunningham 24 W/F wife Keeping house
Joseph Cunningham 2 W/M son

1900 United States Federal Census
Name: John Cunningham
Home in 1900: Civil District 6, Claiborne, Tennessee
Age: 69
Estimated birth year: abt 1831
Birthplace: Tennessee
Relationship to head-of-house: Head
Spouse's name: Sylvinia
Race: White
Occupation: View image
Neighbors: View others on page
Household Members: Name Age
John Cunningham 69 b.1830
Sylvinia Cunningham 71 b. 1828
Marthia Cunningham 17 b. 1872
Mariah A Cunningham 9 b. 1892

There are several other Cunningham families living in the same area but the names are difficult to read.

Olliver {?} W/M 18 Head
Wilson - his son W/M 5 b. 1895

{?} W/M 41 Head b.1859
Matilda - his wife - W/F 40 b.1860
Joseph M. son W/M 22
Margaret daughter W/F 20
Martha {?} G{?} daughter W/F 14
Sarah daughter W/F 11
Harvia {?} R. son W/M 7

Wartham {?} Cunningham W/M 42 - Head of house
Mary G. daughter W/F 19
George M. son W/M 18
Barbara J. daughter W/F 13
William son W/M 11
Barney {?} B. son W/M 9
Hatvia {?} M. daughter W/F 7
James E. son W/M 6
Oskir R. son W/M 4
Martha J. daughter W/F 3
Becky daughter W/F 11 months

1910 United States Federal Census
Name: John Cunningham
Age in 1910: 80
Estimated birth year: abt 1830
Birthplace: Virginia
Relation to Head of House: Head
Father's Birth Place: Virginia
Mother's Birth Place: Virginia
Spouse's name: Silva
Home in 1910: Civil District 5, Claiborne, Tennessee
Marital Status: Married
Race: White
Gender: Male
Household Members: Name Age
John Cunningham 80
Silva Cunningham 87

Hope this helps you with your search.

JR