My suggestion then is that you ask them for a transcript of Buckleys, marriages 1754 - 1812 and 1813 - 1837, baptisms 1813 - 1839, and both sets of burial indexes, total people: 83
And Griffiths, perhaps just the baptisms 1813-1839, of which there are 65.
By email transcripts cost a penny an entry - actually looks like they put a minimum of £3 so you could throw in Griffiths burials etc.
What you are looking for is:
A marriage of ? Buckley to Margaret
Children of ? Buckley and Margaret, who might be younger siblings of Harriet
Death of either Margaret or her husband.
Baptisms of Harriet's children with Thomas.
What was Thomas Griffith's occupation?
Also, I think this may be Margaret's death:
Margaret Buckley, Dec 1857 quarter, E. Stonehouse, Vol 5b page 194.
http://home.clara.net/dixons/Certificates/deaths.htm#COL6 - Clara Dixon's site suggests that it was indeed usual for women to be listed as 'wife of' or 'widow of' on their death certificates, so this may be a way of finding Harriet's father's name.