On 28 Oct 1753 Israel married Lois Brown (50990) , daughter of Thomas Brown (34252) (14 Feb 1691/2-27 Dec 1763) & Deborah Holdridge (33805) (3 Apr 1698-), in Stonington, CT. Born on 1 Sep 1736 in Stonington, CT.211 Lois died aft 1775.

Israel and Lois were second cousins since his maternal grandfather and her paternal grandfather were brothers.

Children of Israel and Lois (Brown) Palmer, born at Stonington:
    i. Jessie Palmer, b. 20 Jul 1754, d. 28 Oct 1825 at Voluntown, CT;
    ii. Margaret Palmer, b. 2 Apr 1756, d. 15 Dec 1808, m. 24 Nov 1771 Melvin Park (b. 13 Feb 1750/1 at Stonington, son of Peter & Lucy (McDowell) Park);
    iii. Aden Palmer, b. ca. 1758, d. 6 Jun 1832 at Corning, Steuben Co., NY, m. 1 Feb 1781 Lois Stanton (b. Nov 1760 at Preston, CT, d. ca. 1830, dau. of Daniel and Dinah Stanton);
    iv. Darius Palmer, b. ca. 1760, m. 1 Dec 1783 Polly Bennet;
    v. Allen Palmer, b. ca. 1762;
    vi. Susannah Palmer, b. ca. 1765; and
    vii. Mervel Palmer, b. ca. 1767, m. 15 Sep 1788 William Breed Nicholson of Newport, RI.