There are some genealogies that claim his parents were John and Grace (Wayford) Briant/Bryant Jr. (Bud Bryant - bry11325 @juno.com)
While other genealogies that I've seen, claim that the John Sr. of Taunton was his father, but the dates refutes this claim. Also, it has been suggested that this Stephen Sr. was the brother of John Sr. of Scituate. I can not find any evidence that proves that they were, or if this John of Scituate is my John. From what I have found, every thing tends to show that they weren't related. For example, there are no "Stephens" in the John Bryant Sr. of Scituate generational line. If they were brothers, you'd think that at least one of the generational lines, would have named one of their sons Stephen.
Plymouth town records were not kept until about 1636, and from these records, I take it that he must have been of age in 1636, for he had his cattle marked and registered in the town book at Plymouth that year. Thus, he had to have been born on or before 1615.
According to Kingman, a Stephen Briant/Bryant was here in 1632, making him about 17 when he came over. He is on the 1643 list of those able to bear arms at Plymouth, and land was purchased by him the same year. 1646 he is on a list of inhabitants of Plymouth. In 1647 he is not on the list at Plymouth, but in Duxbury, married to Abigal Shaw, where she gave birth to their first child, Abigail. In 1654 he is appointed constable of Duxbury, and in 1658, he is back at Plymouth, being appointed surveyor of highways. Thus, sometime between 1654 & 1658 he came back to Plymouth. In 1663 he is appointed constable of Plymouth. 1684, a Stephen is on a list of soldiers of Plymouth (this may be Stephen Jr.), and from that date on, Stephen Sr. is only mentioned in the past tense, so he must have died soon after 1684, making him about 70 years old.