1.  Ann ROSE, b. 27 Nov 1774
  2.  Milley ROSE, b. 8 Mar 1776
  3.  Patience ROSE, b. 4 Mar 1778
  4.  Rachel ROSE, b. 1781
  5.  (Probable Child) ROSE, b. ca. 1783; d. young
  6.  William ROSE, b. 2 Jul 1785
  7.  John ROSE, b. 11 Dec 1787
  8.  Elizabeth ROSE, b. 17/19 Jan 1790
  9.  (Son) ROSE, b. 23 Jul 1792
10.  (Probable Child) ROSE, b. ca. 1794; d. young
11.  Thomas ROSE, b. 11 Dec 1796
12?  June? ROSE, b. 27 Nov 1797?; d. 1798?
13.  Benjamin ROSE, b. 14 Apr 1799

Some say the 9th child is "Ace"; some say he's, "Hosea," but I find the name indecipherable (see below).

1.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):  not found.

2.  Census Index:  Colonial America, 1607-1789 (Broderbund CD-310):  there was a John ROSE in Rowan Co., NC, in 1762, but our subject was too young (æ 12) to have been the person enumerated.  This is the only John ROSE on the CD in Rowan or Surry Co., NC; there were none in Southampton Co., VA.

.  Found via Search on Ancestry.com:

Images of the original pension applications of both John ROSE (Claim No. 18824, 6 Aug 1832) and Widow Lydia ROSE (29 Jul 1843) are online at Ancestry.com multiple times, along with multiple transcriptions, attached to multiple Public Member Trees.  The originals are a tough read, but contain some important genealogical information, including: •  John ROSE, himself, states he was born in 1750 in South Hampton County, Virginia. •  Several deponents confirm that John and Lydia were married in June, 1772, and that Ann was their first child, two years later. •  His military service was extensive, but I just scanned it for genealogical information. •  The images contain a typescript summary dated 25 May 1928 and done by one Winfield SCOTT, "Commissioner," which I found after wading through the originals (aargh!).  I agree with his summary, with the possible exception of the name of the 9th child ("Ace").  See below for an enlargement of that section. •  Since doing the transcription (middle column), I found other transcriptions online.  For the most part we agree, and the differences are trivial, but at least one difference is not, and I've added them to the right.
	John Rose Children ages Ann Rose the Dather of John Rose and Rachil his Wife was born November the 27th in the yeare of our lord __________________1774 Milley Rose the Dauther of John and Rachil his wife was Born the 8th day of march in the yeare of our Lord ______________1776 Pashance Rose the Dauther of John Rose and Rachil his Wife was Born the 4th Day of march in the yeare of our Lord 1778 Rachil Rose was Born in the yeare of our Lord ______________ 1781 William Rose the sun of John Rose and Rachil his Wife was Born the 2th of July in the yeare of our Lord ______________    1785 John Rose the sun of John Rose and Rachil his Wife was born the 11th of December in the yeare of our lord   1787 Alazabeth Rose the Dauther of John Rose and Rachil his Wife was Born the 17th [19th?] of Ja?ary in the yeare of our lord               1790 ? Rose the Sun of John Rose and Rachil his Wife was Born 23th of July the yeare of our Lord ______________  1792 Thomas Rose the sun of John Rose and Rachil his Wife was Born the 11th of December in the yeare of our lord      1796	Notable differences in the other  transcription At the beginning of the line for William, the other transcriber inserts these words:   William Lenoir S7137 I have no idea why because, as you can see, it's not in the original. He shows the 9th child as   Ose [could be Ase]
	June?/Anne? Rose was born November[?] 27th 179? Was [?????????????????................] 1798 [Has anyone managed to decipher this section  If so, please share! ] [Why the space?  Was something written here that faded away?] Benjamin Rose Son [?? ???] was born April ye 14th[?] in the Year of our lord 1799	Shows this child as, "Anne" born November the 27th 1797
	Enlargement of the 9th child's name.  The second part is "Rose," so you're struggling with as few as three letters.  The "Commissioner" says it's Ace; some say Ase or Ose, short for Hosea.