I couldn’t resist a factual reply to include the Tithe Applotment books my past favourite census sbstitute, in case something is useful on Tullyorier or some of the last names mentioned,
1796 Flax Growers
https://www.failteromhat.com/flax/down.phpthere are over 40 entries for Garvaghy no entry for Shaw, they do include
Byrne Edward Garvaghy Down
Byrne Valentine Garvaghy Down
1834 Tithe Applotment books
http://www.irishgenealogyhub.com/down/tithe-applotment-books/garvaghy-parish.phpthese are just one liners name and size of land or value of building or both. originals in PRONI to have 8 entries in one townland.
Down
Byrne, Art.-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, Bernard-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, Danl.-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, Edward-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, Felix-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, Henery-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, Hugh-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, Ilica-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, James-Townland: Corbally Year: 1834-Garvaghy-Down
Byrne, Jno.-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, John-Townland: Corbally Year: 1834-Garvaghy-Down
Byrne, Patt.-Townland: Kilkinamurry Year: 1834-Garvaghy-Down
Byrne, Patt.-Townland: Tullyorier Year: 1834-Garvaghy-Down
Byrne, Widow Townland: Tullyorier Year: 1834-Garvaghy-Down
Maclory, Hugh Townland: Tullyorier Year: 1834
Maclory, Manus Townland: Tullyorier Year: 1834
McClory, Hugh Townland: Tullyorier Year: 1834
McClory, Pat. Townland: Tullyorier Year: 1834
McShane none found
McShean, Hugh-Townland: Tullyorier Year: 1834-Garvaghy-Down
McShean, Rodger-Townland: Tullyorier Year: 1834-Garvaghy-Down
Shaw, Hugh Townland: Carnew Year: 1834
Shaw, John Townland: Enogh Year: 1834
Shaw, Mark Townland: Tullyorier Year: 1834
Shaw, Mathew Townland: Tullyorier Year: 1834
Shaw, Matt. Townland: Tullyorier Year: 1834
Shaw, Michl. Townland: Tullyorier Year: 1834
Shaw, Mick. Townland: Tullyorier Year: 1834
Shaw, Thomas Townland: Tullyorier Year: 1834
Shaw, Thos. Townland: Tullyorier Year: 1834
Shaw, Widow Townland: Tullyorier Year: 1834
Griffiths valuation
using quick index
https://www.failteromhat.com/griffiths.php I didn’t have time to check other last names
Shaw, Anne L: Tullyorior
Shaw, Edward L: Tullyorior
Shaw, Elizabeth L: Carnew
Shaw, John L: Tullinisky
Shaw, John, Jr. L: Tullyorior
Shaw, John, Sr. L: Tullyorior
Shaw, Michael L: Killaney
Shaw, Michael L: Tullyorior N: Irish
Shaw, Michl. L: Tullyorior N: English
Shaw, Wm. L: Kilkinamurry N: and Another f
details including boundaries of homesteads see
http://www.askaboutireland.ie/griffith-valuation/eg Anne Shaw in 1863 in tullyorior has map ref 16 ABA in townland, has 5 acres and house valued at ten shillings pa
while looking up the reference I I realized there is a place named Shawstown the buildings are at the southern end of map ref 20B with blgs marked a&b, also in 19a its ~400ft from the river Bann. the properties starting with map area 16 are not visible to me there isa square block of blank space soory ran out of time
Ros Davies great Co down website has
Shawstown Garvaghy . a house cluster in Tullyorior townland ; 5km SE of Banbridge; the last Shaw died in 1939 old b/w map G7; PNNI V6 p 207
hoping something of interest to you all and I can look up anything for mickwally with his kind offer, then I find out im patronizing him, he knows far more than I including garvaghy and Annaclone have shared blurry borders in the past. I noticed many of my listing had the same last name in Annaclone but ignored in my haste. then also AussieGaz research, I must slowup & read everything sent already before jumping to answer
Good luck to you all onwards