Benjamin Coxe was educated at either Oxford or Cambridge.  After he graduated he received episcopal ordination, and for a considerable period he was a follower of the Romish Arminianism of Archbishop Laud.  By the grace of God his heart was changed and his mind enlightened, and he became a strong Baptist.  He was the son of an English lord bishop; and he was a man of profound learning.  His influence in favor of Baptists was very great all over his country.  He came to Coventry once to encourage the Baptist church; Richard Baxter was then chaplain of the garrison of that town, and a "dispute first by word of mouth, then by writing, about infant baptism," took place between them.  Mr. Baxter evidently had not the best part in the controversy; for when the champion of the Baptists came again to Coventry he was arrested, and Mr. Baxter was charged with using this conclusive argument to quiet Mr. Coxe.  The Kidderminster bishop, while denying the charge, felt the accusation so keenly that he took steps to secure his release.  He was an old man in 1644, but the time of his is unknown.

William Cathcart's Baptist Encyclopedia, 1881

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Some Mistaken Scriptures Sincerely Explained
An Affair Reckoning With Mr. Edwards
An Appendix to a Confession of Faith, London; 1646.

Thesis Concerning Administering & Receiving the Lord's Supper

He who administers the Lord's Supper to one who is a fornicator, or covetous, or an idolater, or a railer, or a drunkard, or an extortioner, does therein commit a very grievous and hateful sin. The children of God must have no fellowship at all with this sin, but reprove it.

The Special Interest of the Elect in Christ & His Saving Grace,

London; 1646. (This is part II of Spilsbury's work, God's Ordinances, The Saints Privilege, the second part is on Particular Redemption against the General Baptists and it was enlarged by Cox in cooperation with Spilsbury).

A Declaration Concerning the Public Debate, London; 1645.