We have no birth, marriage, or death records for Caroline Shackford Banfill but thanks to FindAGrave posting, we believe she is buried in the Allard Cemetery in Madison, New Hampshire near her infant son who lived eight days after her death. Her stone is very difficult to read but you can see the words Caroline, wife of Eli Banfill. His stone says A Son of Eli & Caroline Banfill, DIED Sept 30, 1839, AE 8 ds. Neither of the stones have Caroline's last name -- we find her full maiden name Caroline Shackford on both her daughter Emeline's marriage and death certificate.
We find learn that Caroline's last name was Shackford on her daughter Emeline's marriage and death certificates. On September 8, 1859, Emeline married Ebenezer Colby in Conway, New Hampshire and on her marriage record, her father's name is listed as Eli Banfield and her mother is listed as Caroline Shackford. We'd love to find the original source of this information as the certificate is dated June 30, 1906. Emeline's death occurred on February 14, 1905 in Laconia where she had lived for 5 1/2 years. The death certificate lists her father as Eli Banfill and her mother as Caroline Shackford. We know that Emeline is Eli's daughter because his will states "First. I give and bequeath to my daughter Emeline Colby, wife of Eben Colby, the sum of five dollars."
Unfortunately none of this information helps us find Caroline's parents.
So we've been looking at other information about Banfill/Shackford relationships and find that:
Marion Banfill m Samuel Shackford on Mar 27, 1822 in Eaton, New Hampshire
Gilman Shackford married Hannah Banfill in Conway, NH around 1830 and
Samuel C Banfill married Mary Ann Shackford in 1825 in Eaton, New Hampshire.
Perhaps further research of these relationships will give us some more information about Caroline Shackford and perhaps a further review of the vital records, town records, and probate records of these Banfills or Shackfords or their parents will reveal some more information about this mystery.
Find A Grave, Find A Grave, digital images (http://www.findagrave.com : accessed 8 March 2015), Caroline Shackford Banfill, Find A Grave Memorial# 47476123
Find A Grave, Find A Grave, digital images (http://www.findagrave.com : accessed 9 March 2015), Infant Son Banfill, Find A Grave Memorial# 47476264
New Hampshire, County Probate Estate Files, Eli Banfill Madison, Case 237; "New Hampshire, County Probate Estate Files, 1769-1936," digital images, Family Search (http://www.familysearch.org: accessed 9 March 2015); >Carroll>Case no 234-336 1840-1920>Image 58 of 1640
New Hampshire, New Hampshire, Death Records, 1654-1947, , Emma M Colby m Edwin Colby, 14 February 1905; digital images, FamilySearch, New Hampshire, Death Records, 1654-1947 (http://www.familysearch.org : accessed 2 March 2014).
New Hampshire "New Hampshire, Death and Burial Records Index, 1654-1949," index, Ancestry.com (http://www.ancestry.com : accessed 2 March 2014), Eli Banfill d. 20 Oct 1897.
New Hampshire, New Hampshire, Marriages, 1720-1920, , Emeline Bandfield m. Eben Colby, 9 September 1859; index, FamilySearch (http://www.familysearch.org : accessed 2 March 2014).
"New Hampshire, Marriage and Divorce Records, 1659-1947," digital images, Ancestry.com (http://www.ancestry.com : accessed 14 November 2014), Mary Ann Shackford m Samuel Banfill 5 Nov 1825.
New Hampshire Town Clerk ,Vital and Town Records Family Search, compiled records (http://www.familysearch.org : accessed 10 June 2013), Samuel Shackford m. Meriam Ba