Abner married Elizabeth Francis (59666) , daughter of John Francis & Sarah Borden (49429) (ca 1732-). Elizabeth died in Fall River, MA on 13 Jun 1853.

Children of Abner and Elizabeth (Francis) Cook, born at Tiverton:
    i. Ruth Cook, b. 12 Jan 1787;
    ii. James Cook, b. 7 Jan 1789;
    iii. Samuel Cook, 21 Nov 1790;
    iv. Susanna Cook, b. 7 Sep 1792;
    v. Sarah Cook, b. b. 9 Oct 1794;
    vi. John Cook, b. 15 Mar 1797;
    vii. Abner Cook, b. 9 Jan 1800;
    viii. Paul Cook, b. 17 Feb 1802;
    ix. Borden Cook, b. 17 Apr 1804;
    x. Stephen Cook, b. 8 Mar 1806;
    xi. Joseph Cook, b. 21 Apr 1808; and
    xii. Elizabreth Cook, b. 9 Aug 1810.374