Hi Margaret, 
I looked for tombstones and found on 
www.ancestryireland.coma.  FLEMING   Ballydown Pres   Seapatrick   Ballydown
Ros Davies  ‘Churches’  gives surviving records as baptismal records from 1804 & marriage records from 1845, graveyard attached , oldest stone is 1825; gravestone inscriptions UHF Vol 20; email me for a gravestone lookup.
b.  FLEMING   Scarva St. Pres   Seapatrick   Ballyvally   Down
Ros Davies ‘Churches’  gives surviving records as baptism registers from 1851 & marriage register from 1845; graveyard behind 2nd Presbyterian Church in Ballyvally townland; gravestone inscriptions available UHF Vol 20; email me Ros Davies for a gravestone lookup
Have you exhausted these church records [By the way Ros lives in Australia, if she can do….
I looked at Ballydorn at Killinchy on Ros Davies Co Down website 
http://freepages.genealogy.rootsweb.ancestry.com/~rosdavies/PLACENAMES/BallyAG.htm#Ballyd        Which reads 
‘Ballydorn Ballydoran Ballydown Killinchy 21: 51/63 a townland 2km NE of Killinchy; 355 acres........’
& applied those variant spellings to her entry for 
Ballydown Seapatrick 20: 14/45 a townland 2km SE of Banbridge; 746 acres;.......
I see it was spelt Belidonn in 1712 Ir. Wills Index 1  
http://www.placenamesni.org/resultdetails.php?entry=11715Has anyone experienced an alternative spelling  for Ballydown appearing as Ballydorn in Banbridge area? Your record might still mean Seapatrick not Killinchy
Trying to keep records of all Fleming in the area until proven as non relatives I went back to Griffiths for 1863 and found in Seapatrick Co Down and ran out of time filling in details
Fleming Alexander   Rathfryland Street, Banbridge with map ref 51 47   
Fleming Eliza      Friar's Lane, off Scarva s St Banbridge with map ref 129 31   
Fleming George   Ballydown          has 16 perches with map ref 15
Fleming Isabella   Ballymoney     has 30 perches inc house and garden house valued £1.5 shillings            with map ref 1
Fleming John      Reilly Street,Banbridge      with map ref 51 47
Fleming Mary      Ballydown         has 6 acres with map ref 15
Fleming William   Ballydown   house      has 5 acres   with map ref 17
Keep going the picture is filling up JimG