Yes, there are Tefft genealogies, and published birth records.
The primary source for the birth of William is inRichmond, RI, Land Evidence, 1:3. William's marriage to Mary Kenyon is in RiLE, 1:256. Pardon's birth, RiLE, 1:282-3.
I don't have a primary source for Pardon's marriage to Amy. I show this marriage on pages 131 and 293 of the genealogy I published in 1993, "Ancestors and Descendants of William Browning Greene and Mary Hoxsie Lewis with Allied Families." I have a webpage that lists the libraries that have a copy of the book, http://users.hal-pc.org/~wmewrght/library.htmlhttp://users.hal-pc.org/~wmewrght/library.html
The births and marriage referenced above from the Richmond records were published by Arnold, "Vital Records of Rhode Island." Members of the NEHGS can search these on-line at newenglandancestors.org. Arnold, VRRI is also available for purchase on CD. But these are secondary sources.
You can order microfilm of the Richmond Land Evidence from a local family history center in a Mormon church and verify the accuracy of the dates you show. Again this is a primary source.
Three descendants of William's Tefft's parents have been DNA tested, so DNA tests can also show if a patrilineal Tefft descendant shows a recent common ancestor with these Teffts.
How are you related to these Teffts?
We share Tefft, Greene and Kenyon ancestors. There are problems with some of the information available on line with respect to each of these families. You are wise to ask for documentation.
If you are willing to share information on your descent, I can explore in more depth what I have on our related ancestors and see if we can work out some evidence for Pardon's marriage to Amy.