I've seen reports on the internet that a William Conyers (b about 1675) married an Anne Bearsoncit and had a son Henry Conyers b 1702. Whether or not it is true, I have no idea. However, most are reporting this Henry as the Capt. Henry that died in 1733, so this cannot be if the Capt. Henry Conyers that died in 1733 is the same Henry that gave the deposition stating he was of age to be born around 1681.
Is it possible that William and Capt. Henry are bothers, and that William had a son Henry in 1702 that was Capt. Henry's nephew?