Other than Augustine, which Church Fathers have directly influenced John Calvin's teaching of "double-predestination?" "By predestination we mean the eternal decree of God, by which he
  determined with himself whatever he wished to happen with regard to
  every man. All are not created on equal terms, but some are
  preordained to eternal life, others to eternal damnation; and,
  accordingly, as each has been created for one or other of these ends,
  we say that he has been predestinated to life or to death." (Calvin,
  Institutes, Book III)


I've noticed, from my theological discussions with various Calvinists,  that the "go-to" early Church Father figure concerning the Calvinist view of double-predestination is St. Augustine.

Who else in the early Church directly influenced Calvin's doctrinal formulation of predestinarianism.  

I prefer references to writings of the Church Fathers preceding St. Augustine, but any Patristic texts will do...as long as they are not Augustine's.
From Calvin's Institutes of the Christian Religion, Book 2, Chapter 2, Section 4


  Moreover although the Greek Fathers, above others, and especially Chrysostom, have exceeded due bounds in extolling the powers of the human will, yet all ancient theologians, with the exception of Augustine, are so confused, vacillating, and contradictory on this subject, that no certainty can be obtained from their writings.


Clearly Calvin felt that only Augustine understood predestination correctly. But, in the same section of the Institutes he invokes at least 3 other Church fathers:


Cyprian


  What, then, is meant by Cyprian in the passage so often lauded by Augustine, “Let us glory in nothing, because nothing is ours,” unless it be, that man being utterly destitute, considered in himself, should entirely depend on God?
  Institutes, Book 2, Chapter 2, Section 9
  Here Calvin is referring to Chapter 36 of A Treatise on the Gift of Perserverance by Augustine. Augustine is in turn quoting Cyprian's Testimonies Book III Section 4

Eucherius of Lyon
In the next sentence Calvin invokes Augustine and Eucherius:


  What is meant by Augustine and Eucherius, when they expound that Christ is the tree of life, and that whoso puts forth his hand to it shall live; that the choice of the will is the tree of the knowledge of good and evil, and that he who, forsaking the grace of God, tastes of it shall die?

John Chrysostom
And in the following sentence he quotes John Chrysostom


  What is meant by Chrysostom, when he says, “That every man is not only naturally a sinner, but is wholly sin?” If there is nothing good in us; if man, from the crown of the head to the sole of the foot, is wholly sin; if it is not even lawful to try how far the power of the will extends,—how can it be lawful to share the merit of a good work between God and man?



It's hard to say whether these other fathers directly influenced the doctrine of double predestination since so few of them, by Calvin's research, taught predestination at all. The closest would be Cyprian especially since I was able to find Cyprian's own books. The reference to John Chrysostom is interesting since Calvin condemns him and then quotes him to support his doctrine.