I am trying to find out which Josiah Allen married Mary Flagg on 29 Dec 1748 (Weston Vital Records).I have found a Josiah born 31 Mar 1708, son of Ebenezer and Elizabeth (Eddy) Allen and a Josiah born 30 Apr 1719, son of Nathaniel and Lydia (Brewer) Allen.
Children of Josiah and Mary Allen: Lydia b. 2 Nov 1749 Nathaniel b. 29 Aug 1751 Mary b. 19 Mar 1754 Josiah b. 1 may 1756 ? Matthew b. 8 Feb 1759 Martha b. 8 Feb 1759 (Weston Vital Records-Church Records) Lucy b. 11 Apr 1761
The childrens names seem to match the Josiah born in 1719.