There are "Stillwaters" in Chautauqua, Essex, Herkimer, Oswego, Putnam, and Saratoga Cos., NY.  But if Caleb was born in Vermont, Gideon was most likely born in the Stillwater in Essex Co., NY, which county borders Vermont.  As the crow flies, this Stillwater is only about 65 miles NW of Pawlet.

Modena's birth and death dates appear to be from a tombstone, which means Modena must have been fibbing about her age later in life because there is no way she married at age 11.

— born in Eddyville, Livingston [now Lyon] Co., KY:
  3.  Robert Livingston COBB, b. 1804/5  {45, Christian Co., KY} 
  4.  (Daughter B) COBB, b. 1804-1810
  5.  (Dr.) [Dyer?] Joshua COBB, b. 19 Apr 1809  {41, KY} 

— born in Eddyville, Caldwell [now Lyon] Co., KY:
  6.  Mary Willard COBB, b. 1810  {40, KY} 
  7.  Hannah Chittenden COBB, b. 25 Dec 1811; d. 16 Feb 1841 
  8.  Persis C. COBB, b. 1812/3, KY {37, KY} 
  9.  Gideon Dyer COBB, b. 3 May 1818  {32, KY} 
10.  Aurelia Skinner COBB, b. 17 Oct 1819  {30, Caldwell Co., KY} 
11.  Giles L. COBB, b. 1823 

Robert was probably mistaken about being born in Christian Co. because 1) his father never appears on the Christian Co. tax rolls, 2) his father came to Livingston [now Lyon] Co. with Col. Matthew LYON ca. 1801, and 3) Livingston Co. was formed from Christian Co., KY, by 1798, so it's not just a matter of a county name change.

1.  Census Index:  Colonial America, 1607-1789 (Broderbund CD-310):

1785

Cobb, Elkanah

VT

Rutland Co.

Pawlet

p. 143

Other COBBs in Rutland Co. were:  Ebenezer, John, John, John, and Joshua.

2.  Census Index:  U.S. Selected Counties, 1790 (Broderbund CD-311):

1790	Cobb, Elkanah	VT	Rutland Co.	p. 41	04-05-04-00-00
1790	Cobb, Gideon	VT	Rutland Co.	p. 41	01-00-01-00-00

Other COBBs in Rutland Co. were:  Ebenezer, John, John, John Jr., Joshua, and Justus.
Gideon's numbers indicate a newlywed couple with, as yet, no children:

Gender and Type	Age Class	Therefore Born	Individuals Inferred
1 free white male	16 or over	in or bef. 1774	= Gideon (b. 1773)
1 free white female	all ages	in or bef. 1790	= Modena (b. 177?)

3.  Census Index:  U.S. Selected Counties, 1800 (Broderbund CD-312):  not found, anywhere, but the 1800 census of KY was destroyed.  The COBBs in Pawlet, Rutland Co. were:  John, Joshua, and Mary, who appears to be Elkanah's widow.  Supposedly, the colony from Vermont led by Col. Matthew LYON did not arrive at the site of Eddyville until 1801; yet, clearly, Gideon is no longer in Vermont.

4.  1810 Census Index/Images (online at Ancestry.com; Image #5 of 19; extracted by Diana Gale Matthiesen with thanks to Terry Reigle for correcting my former misinterpretation of this record):

1810

KY

Caldwell Co.

Town of Eddyville

p. 7/393

Ln. 1

Cobb & Clarke

30020-11010-00

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
3 males	9 or under	1800-1810	= Joshua (b. 1809) = Robert (b. 1804/5) = Caleb (b. 1796/7)
2 males	26-44	1765-1784	= Gideon (b. 1773) = Mr. Clarke
1 female	9 or under	1800-1810	= Daughter B
1 female	10-15	1794-1800	= Daughter A
1 female	26-44	1765-1784	= Modena (b. 177?)

Caleb appears to be in the wrong age-class.  The "Clarke" is presumably kin of Modena's.  Listed four lines above Matthew LYON.  The Town of Eddyville consisted of only 27 households.

5.  1820 Census Index and Digital Images (online at Ancestry.com; Image #1 of 1; extracted by Diana Gale Matthiesen):

1820

KY

Caldwell Co.

Eddyville

p. 46

Gideon D Cobb

120102-22101-0-000

no slaves

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	9 or under	1810-1820	= Gideon (b. 1818)
2 males	10-15	1804-1810	= Joshua (b. 1809) = Robert (b. 1804/5)
1 male	19-25*	1794-1801	= Caleb (b. 1796/7)
2 males	45 or over	in or bef. 1775	= Gideon (b. 1773) = Mr. Clarke?
2 females	9 or under	1810-1820	= Aurelia (b. 1819) = Persis (b. 1812/3) = Hannah (b. 1811)
2 females	10-15	1804-1810	= Mary (b. 1810) = Daughter B
1 female	16-25	1794-1804	= Daughter A
1 female	45 or over	in or bef. 1775	= Modena (b. 177?)
*In the 1820 Census, the third column is age class 16-18 and the fourth column is age class 16-25; therefore, any individual in column three is duplicated in column four.  By subtracting the number in column three from the number in column four, you can create an age class "19-25."

Listed 21 lines down from brother, John COBB.  Eddyville consisted of only 31 households.

6.  1830 Census Index and Digital Images (online at Ancestry.com; Image #49-50 of 88 — indexed "Cool"; extracted by Diana Gale Matthiesen):

1830

KY

Caldwell Co.

Eddyville

pp. 161B-162A

Gideon Cobb

011 170 010 - 001 201 000

001 000 - 000 100

These data indicate:

No., Race, Gender	Age Class	Therefore Born	Individuals Inferred
1 white male	5-9	1820-1825	= Giles (b. 1823)
1 white male	10-14	1815-1820	= Gideon (b. 1818)
1 white male	15-19	1810-1815	= ? (not a son)
7 white males	20-29	1800-1810	= Joshua (b. 1809) = Robert (b. 1804/5) =
1 white male	50-59	1770-1780	= Gideon (b. 1773)
1 white female	10-14	1815-1820	= Aurelia (b. 1819)
2 white females	15-19	1810-1815	= Hannah (b. 1811) = Persis
1 white female	30-39	1790-1800	= Modena (b. 177?)
1 male slave	24-35	1794-1806	= ?
1 female slave	36-54	1775-1794	= ?

Modena is telling a whopping lie about her age.  Listed four lines above brother, John COBB, who is listed nine lines above our subjects' daughter, Mary (COBB) CLARK. 

7.  Anon.  1991.  The 1795 Census of Kentucky [as constructed from tax lists].  T.L.C. Genealogy, Miami Beach, FL (said to include every extant tax list from the state of Kentucky for the year 1795):  not found.  The only COB/COBB/COBBS in KY were James, Robert, William, and John.

8.  A.B. Willhite.  [n.d.]  Christian Co., Kentucky, Tax List, 1804-1809.  (self-published; available from author at 4396 Coopertown Rd., Russellville, KY 42276, or from the Christian County Genealogical Society, Hopkinsville, KY):  not found.  The only COBB in the book is Jesse COBB on Pond River, in eastern Christian Co.

9a.  Lon Arneld Bostick, Sr. & James Taylor Killebrew.  1985.  County Court Order Book "A" for Christian County, Kentucky for the Years 21 March 1797 - 29 August 1805...  Christian County Genealogical Society (1101 Bethel St., Hopkinsville, KY 42240):  not found.  There are no COBB entries in the book.

9b.  Lon Arneld Bostick, Sr.  1987.  County Court Order Book "B" Part 1 for Christian County, Kentucky, for the years 14 Oct 1805 - 12 Sep 1809 for a County Court held at Town of Hopkinsville. Christian County Family and History Research Society (4465 Cadiz Rd., Hopkinsville, KY 42240):  not found.  There are no COBB entries in the book.

10.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).

11.  Terry Reigel.  Reigel Roots. [link died]  And email from Terry.