Hi Karina,
Walkingshaw would still be a name from that general area - I looked at
www.bt.com and found one in Saintfield which is not too far from Ballygowan. Perhaps they could help.
Regarding the burial, there is a large Presbyterian Church in Ballygowan with an attached cemetry:
__http://www.presbyterianireland.org/congregations/ballygowan.html
I'm sure they will have a record of who is buried there, I see there is an email address. I think the nearest C of I church would be at either Kilmood or Saintfield - guess Saintfield would be best bet going on what Pat found.
Hope this helps