Church records indicate she died in 1819 at the age of 67, which puts her birth before June 1752.Hathaway-4200 marries in 1759, when Hathaway-4200 (per church records) would have been almost 7, and having her first child at the same tender age. Hathaway-4200 gets around this problem by winding back Miriam's date of birth, and only cites the above linked Church record, which does not support the earlier date of birth.
That is a tough one. Your Morristown Presbyterian church reference was very helpful. Unfortunately, it guessed wrong on an important point. Note that on p. 101, it has Abraham Hathaway's daughter as "Miriam; B. 31 March 1751; [? m. Joseph Beers, q.v.]" Turns out that the question mark is very important. It looks like they guessed incorrectly as to which Miriam Hathaway married Joseph Beers (p. 18) because there is another Miriam Hathaway of similar age, daughter of Simeon (p. 104). She's the one married Joseph Beers. The reason I say this is because of Richard Hathaway's RW pension application. Miriam daughter of Abraham had brothers Richard and Nathan. The other Miriam did not. The application notes a brother Nathan and "his sis Meriam Lossey of Morris Co NJ". That seems to be the smoking gun.
Just as I was figuring this out I saw the Family Search tree that has Miriam Beers as the daughter of Simeon. I also found a nice write up on Ancestry of an smyers147 who had it all figured out (link). If you don't have an Ancestry subscription, let me know and I'll send those documents to you (no sharable link).
Here's the Richard Hathaway pension application (widow Abigail) if you want to plow through it: https://search.ancestry.com/cgi-bin/sse.dll?dbid=1995&h=70727&indiv=try&o_vc=Record:OtherRecord&rhSource=2539