Hi Tom,
Not sure if you meant you don't have a marriage between John McBurnie & Ann Irving, or just between William McBurnie and Helen Hannah - but in any case the IGI has two records for a John McBurnie & Ann Irving marriage (one in 1824 and one in 1823) which illustrate the problems with searching because of the various spellings and interpretations of surnames/forenames -
Example - one record is Annie Irvine/John Burnie
and another is Ann Irvine/John MCBirnie
both in Troqueer, Kirkcudbright, SCT
I have been searching Mary Hanna, and found her as Mary Harris, Mary Hannay, Mary Hannah - but I will see what I can find for your William McBurnie and Helen Hannah - any idea as to marriage date range???
best,
drakes