From the five census records my hypothesis is that Thomas was born at Pencoed, in the parish of Coychurch, in 1808-1809.
Baptisms
I found that between 1805 and 1812 there were at least 4 Thomas Morgan baptisms at/near Coychurch:
- 1805 at Coychurch with parents Morgan and Catharine - this seems to be the same baptism as that below.
"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VFCV-XHH : accessed 6 March
2016), Thomas Morgan, 1805; Baptism, citing Coychurch, Glamorgan,
Wales, Glamorgan Family History Society, Cardiff.
- 11 Feb 1805 at Coychurch with parents Thomas and Catharine - indexed at FreeREG and appears to be the same baptism that is indexed at FamilySearch without the Parish name. That links to a FindMyPast image showing the father's first name to Morgan rather than Thomas.

"Wales, Glamorganshire, Parish Registers, 1538-1912," database,
FamilySearch (https://familysearch.org/ark:/61903/1:1:KCY4-ZT3 :
accessed 6 March 2016), Thomas Morgan, 11 Feb 1805, Baptism; from
"Parish Records Collection 1538-2005," database and images, findmypast
(http://www.findmypast.com : 2012); citing , Glamorganshire, Wales,
The National Archives, Kew, Surrey.
- 21 Sep 1808 at Coychurch with parents Thomas and Ann - indexed at FreeREG and appears to be the same baptism that is indexed twice at FamilySearch. The first only mentions the County and not the Parish but links to the FindMyPast image below the FamilySearch citation. The second includes the Parish.
"Wales, Glamorganshire, Parish Registers, 1538-1912," database,
FamilySearch (https://familysearch.org/ark:/61903/1:1:KCY4-DBP :
accessed 5 March 2016), Thomas Morgan, 21 Sep 1808, Baptism; from
"Parish Records Collection 1538-2005," database and images, findmypast
(http://www.findmypast.com : 2012); citing , Glamorganshire, Wales,
The National Archives, Kew, Surrey.

"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VFCV-XHP : accessed 6 March
2016), Thomas Morgan, 1808; Baptism, citing Coychurch, Glamorgan,
Wales, Glamorgan Family History Society, Cardiff.
- 17 Jun 1809 at Bridgend with parents John and Catherine (which has a currently unreachable FindMyPast image)
"England and Wales Non-Conformist Record Indexes (RG4-8), 1588-1977,"
database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:FQ4N-R6G : accessed 6 March
2016), Thomas Morgan, 17 Jun 1809, Birth; citing p. 14, Bridgend,
Glamorganshire, record group RG4, Public Record Office, London.
- 2 Oct 1810 at Coychurch with parents Evan and Jane - indexed at FreeREG
"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VFH5-PDK : accessed 6 March
2016), Thomas Morgan, 1810; Baptism, citing Coychurch, Glamorgan,
Wales, Glamorgan Family History Society, Cardiff.
The 1808 baptism is the one closest to the expected birth date. It also fits best when applying the Welsh Naming Pattern to the order of his children’s births because his first son was Thomas and his second daughter was Ann, suggesting that Thomas’ parents would have been named Thomas and Ann.
The 1809 baptism would suggest Thomas naming his third son after his father and his third daughter after his mother which not quite what be expected when applying the Welsh Naming Pattern.
The 1810 baptism would be to parents whose names were not used for any of Thomas’ five boys and six girls, and so to me that seems unlikely.
The 1805 baptism would appear to be a few years too early, but if the father was Morgan and not Thomas then it suggests that Thomas did not name any of his five sons after his father, and named his third rather than second daughter after his mother.
My tentative conclusion from examining the baptism records is that my 3rd great grandfather Thomas Morgan was baptised on 21 Sep 1808 at Coychurch to Thomas and Ann.
Burials
I found that between 1805 and 1831 (when my 3rd great grandfather married) there were at least 3 Thomas Morgan burials at/near Coychurch:
- 1819 - buried at Coychurch but aged 22 so would appear to be at least 8 years too old
"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VFHS-TBG : accessed 6 March
2016), Thomas Morgan, 1819; Burial, citing Coychurch, Glamorgan,
Wales, Glamorgan Family History Society, Cardiff.
- 1819 - buried at Coychurch but aged 19 so would appear to be at least 5 years too old
"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VFCV-GFH : accessed 6 March
2016), Thomas Morgan, 1819; Burial, citing Coychurch, Glamorgan,
Wales, Glamorgan Family History Society, Cardiff.
- 1825 - buried at Coychurch but aged 66 so far too old
"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VFCV-GF8 : accessed 6 March
2016), Thomas Morgan, 1825; Burial, citing Coychurch, Glamorgan,
Wales, Glamorgan Family History Society, Cardiff.
There appear to be no burial records demonstrating that any of the four Thomas Morgan candidates died as infants/children so I need to assume that all reached adult and may have married.
Marriages
I found that between 1825 and 1850 there were at least 2 Thomas Morgan marriages at/near Coychurch:
- 1830 at Coychurch to Elizabeth Howell
"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VFCC-WFF : accessed 6 March
2016), Thomas Morgan and Elizabeth Howell, 1830; Marriage, citing
Coychurch, Glamorgan, Wales, Glamorgan Family History Society,
Cardiff.
- 1835 at Coychurch to Elizabeth Morgan
"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VF41-7SK : accessed 6 March
2016), Thomas Morgan and Elizabeth Morgan, 1835; Marriage, citing
Coychurch, Glamorgan, Wales, Glamorgan Family History Society,
Cardiff.
These marriages may belong to two of the alternate Thomas Morgan candidates, but more marriages may need to be considered because my 3rd great grandparents Thomas and Margaret were born in Pencoed/Coychurch and Bristol respectively, and appear to have married on 20 Aug 1831 at St Brides Minor that is a few miles away.
"Wales, Glamorganshire, Parish Registers, 1538-1912," database,
FamilySearch (https://familysearch.org/ark:/61903/1:1:KCBX-R1B :
accessed 6 March 2016), Thomas Morgan and Margaret Morgan, 20 Aug
1831, Marriage; from "Parish Records Collection 1538-2005," database
and images, findmypast (http://www.findmypast.com : 2012); citing St
Bride's Minor, Glamorganshire, Wales, The National Archives, Kew,
Surrey.
The image of that marriage is available at FindMyPast and shows that Thomas is of Coychurch parish:

I have noted that one of the witnesses to this marriage was William Morgan. It seems probable that he would have been the father or brother of either Thomas or Margaret (they both had the surname Morgan) which may help confirm their identities. Thomas and Margaret named their second son William so perhaps this was Margaret's father. Neither William nor Margaret signed, whereas Thomas did. The baptism I have for Margaret is on 28 Aug 1808 at St James, Bristol to William and Jane, and while that may require further investigation it seems to fit. That Margaret seems to have also had a brother called William baptised in the same church on 15 Jul 1804.
Sibling
Acting on a tip in @HarryVervet's answer I looked for possible siblings for Thomas son of Thomas and Ann and found a baptism indexed twice (and a FindMyPast image) for Ann who was baptised on 23 Mar 1814 to Thomas (a Collier) and Ann, who were living at Ty Bryn.
"Wales, Glamorgan Parish Registers, 1558-1900," database, FamilySearch
(https://familysearch.org/ark:/61903/1:1:VFHR-K6M : accessed 7 March
2016), Ann Morgan, 1814; Baptism, citing Coychurch, Glamorgan, Wales,
Glamorgan Family History Society, Cardiff.
"Wales, Glamorganshire, Parish Registers, 1538-1912," database,
FamilySearch (https://familysearch.org/ark:/61903/1:1:KCY4-DHH :
accessed 7 March 2016), Ann Morgan, 23 Mar 1814, Baptism; from "Parish
Records Collection 1538-2005," database and images, findmypast
(http://www.findmypast.com : 2012); citing Coychurch, Glamorganshire,
Wales, The National Archives, Kew, Surrey.

I think Ty Bryn is either a misspelling of Tre-Bryn or a variation of it, but in any event from Google Maps two modern locations with those spellings are only a few hundred metres apart:

Conclusion
My conclusion from examining census, baptism, burial and marriage records, and taking into account the locations of place names mentioned, as well as Welsh naming conventions for children, is that my 3rd great grandfather Thomas Morgan (a Labourer and Farmer), who lived for the latter half of his life at Tre-bryn, was baptised on 21 Sep 1808 at Coychurch as the son of Thomas (a Collier by occupation) and Ann, who were of Tre-bryn (or at least Ty Bryn), Pencoed in the parish of Coychurch.
These places are found to be in close proximity using 19th and 20th century maps from the Vision of Britian Historical Maps site:

