Morag, I think the churchyard is still there, tucked in behind what is now the Baptist Church of Stranraer on Bellevilla Road. The churchyard is round the back I think on Thistle Street.
Hopefully, these two photos will help you with bearings
www.geograph.org.uk/search.php?i=41372558On the second photo of Bellevilla Road and Thistle Street, the churchyard is just behind the church building, running along that stone wall.
Google maps/streetview show it really well.
Some of the history showing for the location re churches:
Stranraer Bellevilla Burgher (later United Secession, U.P; now Baptist) Church www.scran.ac.uk/database/record.php?usi=000-000-738-181-CEven if there is no stone to be found for your friend's ancestors, hopefully photos from the cemetery will help. You may also find other types of records such as burial register entries, hire of the mortcloth etc. which might all help.
Monica