No birth record found. This source suggests Beulah was born before Jan 1757 based on an analysis of warnings out.
8 May 1753 Jonathan, wife and 4 children warned out of Mendon [Ichabod not mentioned].
14 May 1754 warned out of Grafton [Hephzibah baptized there 6 months later].
1 Nov 1757 Jonathan wife and six children warned out of Uxbridge [this source assumes Ichabod not included (possibly questionable assumption, see next warning) and sixth child was Beulah]
2 May 1760 Jonathan, wife Susanna, children Ichabod, Jonthan, Susanna, Jemimah, Hepzibah and Beulah warned out of Upton [Beulah explicitly named, so definitely born by this date]
16 Aug 1763 Jonathan and Susanna and children Jonathan, Susanna, Jemima Hepzibah and Beulah warned out of Shrewsbury