Born in Stamford, Davenport graduated from Yale in 1732.His first wife was Elizabeth Huntington (daughter of Jabez
Huntington of Windham) whom he married in 1750. Elizabeth had five children before her death in 1773. In 1776 Davenport married Mrs. Martha Fitch.
Davenport served as a Stamford selectman from 1746 until 1777 and then served as town treasurer for two years as well as serving as a deacon in the First Congregational Church of Stamford from 1759 until 1789.
Davenport served as a representative in the General Assembly from 1747 to 1766 and was then elected to the upper house where he served until 1784. He served on the Council of Safety from 1777 until 1783. During the New York campaign, Davenport cared for sick soldiers returning home. He housed many in his own house and found housing and care for many more.