Chasing up and down the lineage mentioned in Rootsweb, it's conceivable that we could find the common ancestor that is missing documentation. I can find some additional data up to William C Coverdale, born 1635 in Yorkshire or Whitby, Yorkshire. Married Mary Sawyer/Sayer.
His father is the questionable one - someone has stitched together several generations in one fell swoop. Myles, born 1488, married around 1540, kids born around 1542 and 1546, appear to have given birth to William - born 1635. So his child, according to this link, would have been fathered by the son of Myles (Roger or Thomas) when Roger or Thomas was about 90 years old. Hmmm...