Some sources have one or more of the boys born in Greene Co., TN, but tax rolls and the census show their father living in Washington Co. from at least 1792 to 1832 — unless we've got more than one John RUBLE to deal with here.  I believe the estimated birth years for the daughters and their parents, as given in some secondary sources, are much too early.

1.  Census Index:  U.S. Selected Counties, 1800 (Broderbund CD-312):  there are no extant schedules for Tennessee.

2.  Census Index:  U.S. Selected Counties, 1810 (Broderbund CD-313):  there are no extant schedules for Tennessee, except for Grainger and Rutherford Cos.

3.  Census Index:  U.S. Selected Counties, 1820 (Broderbund CD-314):  Washington Co., TN, not on this CD.

4.  Census Index:  U.S. Selected Counties, 1830 (Broderbund CD-315):

1830 Census	Ruble, John E.	TN	Washington Co.	p. 26
1832	Ruble, John E.	TN	Washington Co.

Also in Washington Co.:  John E.'s sons, Henry E. RUBLE and John [W.] RUBLE, plus Duke, John S., Henry, Margaret, and Martha RUBLE. 

5.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):  for the state of Tennessee, surnames from the mid-H's through Z are missing from this CD (see my WARNINGs regarding the Broderbund databases).  [These surnames are also missing from the database at Ancestry.com.] 

6.  Marjorie Hood Fischer.  1996.  Tennesseans before 1800, Washington County.  Frontier Press, Galveston, TX.  Anyone with kin in Washington Co., TN, before 1800 needs this book!  The book is an index, not the records themselves, but the entries are voluminous and exhaustive — and include many for the RUBLEs.  I'm here condensing those for John, as found on pp. 260-261:

Name	Record Type	Number of Records
Rubb, John	Tax List	1798
Rubel, John	Tax List	1792
Rubil, John	Tax List	1795
Ruble, John	Tax List	1793, 1796, 1797
Ruble, John	Deed	5
Ruble, John	Co Court Minutes	1
Ruble, John	Sup Court Minutes	1
Ruble, John	County Pleas	2

These records are available on microfilm at the Tennessee State Library in Nashville and the LDS Family History Library.  The book, page, and microfilm roll numbers are given by Fischer for each entry.

7.  Byron Sistler & Barbara Sistler.  1987.  Early East Tennessee Marriages, Vol. 2, Brides.  Byron Sistler & Assoc., Inc., Nashville, TN.  On p. 317:

Ruble, Elizabeth to Alexander McGinty 2-1-1817 [Wa] Ruble, Margaret to Barnibas May 12-4-1818 [Wa] Ruble, Mary to Turner Smith 2-21-1809 [Wa]

Is this Margaret our subject's daughter?

8.  WorldConnect (online at RootsWeb.com).  Lewis Ruble citing J.L. Brumit of Darian, CT, who extracted the following from:
Washington County, Tennessee, Deed Book 31, p. 436.

...Andrew Brumit and Caterine Brumit, his wife formerly Catherine Ruble, heir of Martha Ruble, deceased.

9.  LDS.  Family Search: Internet Genealogy Service: Ancestral File.