One volume of The Documentary History of the Ratification of the Constitution: Ratification by the States covers New Hampshire:
The New Hampshire volume is not currently available for free through the University of Wisconsin Digital Collections. Volumes are are made available two years after publication; the New Hampshire volume was published in 2017. However, the New Hampshire volume is available through the project website of the University of Virginia Press if you or your institution has a subscription, or may be available in a library near you.
Alfredus, Exeter Freeman's Oracle, 18 January 1788, page 86 (subscription required)