http://www.warehamhistory.com/WarehamGenWeb/WrhmVR.htm :
"On 10 July, 1739, a part of Rochester, Mass., and a part of Plymouth called Agawam were incorporated as the town of Wareham. The earliest vital records of the new town are found in a book now labeled 'Town of Wareham, Town Records 1739-1805'"

Her marriage was in 1741, so Elizabeth, born about 1716-1721, may have been born in Plymouth, but in the part that was set off to become Wareham.

Possibilities from Plymouth Vital Records (at Ancestry):

Elizabeth born the 28th of May 1723 (of Thomas Swift and Thankfull Swift his wife)
Elizabeth born about the 22th Jan. 1717/8 (of Samuel Swift & Abigal Swift his wife)
Elizabeth born Aug. 22 1722 at Yarmouth (of Ebenezer Swift & Mary his wife)

Elizabeth's 3rd child was named Abigail, and she would have been under 20 to be married in 1741 and born after 1721, so I'm going with the Elizabeth born Jan. 1718 to Samuel and Abigail. Need to verify somehow that Samuel was living in the part of Plymouth that got split off to Wareham.

• Married: 06 Sep 1741 in Wareham, Massachusetts
• Note:

  http://www.warehamhistory.com/WarehamGenWeb/MI.htm (book:page):
  1:275 Morse, Gershom of Middleborough and Swift, Elizabeth of Wareham int. 08-Aug 1741
  1:271 Morse, Gershom of Middleborough and Swift, Elizabeth of Wareham m. 06-Sep 1741

1. Job Morse b: 02 Jan 1756 in Wareham, Massachusetts c: 18 Jan 1756 in Wareham, Massachusetts