There are a lot of men named Gardner Davis in the early 1800's. American Ancestors (NEHGS), Tyringham Births, V1, p. 24, transcript in Massachusetts Vital Records, 1620-1850, lists the Gardner in the profile:
Gardner Jr., s. Gardner and Lydia, May 31, 1788
other births to those parents include:
Ansel, s. b. Feb. 19, 1794
Lydia, d. b. Jan 31, 1796
Mehitabel, d. b. Dec. 15, 1791
Peter, s. born Feb. 6, 1787
Ruth, d. born Jan. 13, 1798
Shora, s. born Apr. 9, 1790
Gardner Davis appears on the U.S. Census in Tyringham in 1790, 1800, and 1810. The 1810 census includes 9 family members, so there apparently were no additional children:
Free white persons - Males - 10 thru 15: 1
Free white persons - Males - 16 thru 25: 3
Free white persons - Males - 45 and over: 1
Free white persons - Females 10 thru 15: 2
Free white persons - Females 16 thru 25: 1
Free white persons - Females 45 and over: 1
Number of Household members under 16: 3
Number of Household members over 25: 2
Number of Household members: 9
Year; 1810 Census Place: Tyringham, Berkshire, Massachusetts; Roll: 17; Page: 199; Image: 00175; Family History Library Film: 0205625