Hi Billy
Catherine and James's marriage took place prior to official registration in 1855 in Scotland. Their marriage is recorded on the Old Parish Registers (OPRs). On IGI you will see it shows the entry is an actual extract from the OPRs. Sadly, most entries in the OPRs will simply be a one liner with the bride and groom's name and not much else. Very seldom were the parents' names included. You could order a copy of the entry from the OPR direct from Scotlands People (or order the film for this register at your LDS centre) but be aware it is a lucky dip!
Another way to try and gather info is to look at the names of their children and see whether they followed Scottish naming patterns (first son after father's father, first daughter after mother's mother etc.). From IGI, these children show for them:
1. JOHN GRAHAM Birth: 12 APR 1842 Falkirk, Stirling, Scotland
2. CATHERINE GRAHAM Birth: 27 FEB 1849 Falkirk, Stirling, Scotland
3. JAMES GRAHAM Birth: JUL 1845 Falkirk, Stirling, Scotland
4. MARY GRAHAM Birth: 28 JAN 1841 Falkirk, Stirling, Scotland
5. RACHEL GRAHAM Birth: 28 OCT 1843 Falkirk, Stirling, Scotland
For example, using the naming pattern above, their first son was called John and second daughter was called Rachel. If the theory works (and it doesn't always!) James Graham's parents would be John and Rachel. There is a submitted entry on IGI that would fit:
JAMES GRAHAM Birth: 19 DEC 1813 Falkirk, Stirling, Scotland
Parents: Father: JOHN GRAHAM Mother: RACHEL WILKINSON
If James and Catherine died in Scotland, you should be able to find their death certs which will confirm their parents' details. There is one entry on SP for the death in Stirlingshire of a Catherine Graham, other name Amos, in 1879 who is showing as born in 1812 which looks a strong contender!
Regards.
Monica