Two church fathers who (a) reject Origen's universal salvation and (b) are not influenced by Augustine are Basil (d. 379) and Chrysostom (d. 407). Their theological systems, however, are not nearly as well-developed as that of Augustine with respect to the interaction of divine and human will. More speculatively, Pelagius (d. 420?) may also have assumed anti-universalistic premises in developing his anti-Augustinian theology.

Basil

Brian Edward Daley, The Hope of the Early Church, remarks that Basil was "an admirer of Origen in his younger days" (81) and was closely familiar with his work. However, in his later years he became "more severe in his own expectations of the future" and found the teaching of judgment valuable for the spiritual development of Christians.

Basil deals with this most clearly in Question 267 of his Shorter Rule, where he calls Matthew 25:46 ("These shall go away into eternal punishment") an "explicit statement" that there is no end of punishment. The editor of a critical edition, Anna Silvas, comments on the controversy, noting that Basil affirms Origen's "alienation of God" understanding of hell, but rejecting the idea that it has an end (418). Daley summarizes Basil's comments:

To imagine that the fires of hell will ever go out, he insists, is a deceit of the devil: eternal punishment can no more come to an end than can eternal life. (81)

Thus, we can see Basil rejected universalism. However, he seems to do so on scriptural and prudential grounds, unlike Augustine who developed a theology in defense of an eternal hell.

Chrysostom

Like Basil, Chrysostom saw eschatological themes as a crucial part of his preaching ministry. And thus he makes repeated reference to them, and explicitly teaches eternal punishment, for example, in his Homilies on Matthew, 43:

But we have a sea of fire, a sea not like that, either in kind or in size, but far greater and fiercer, having its waves of fire, of some strange and horrible fire. A great abyss is there, of most intolerable flame. [...] Concerning that day, hear the prophets, saying, “The day of the Lord is incurable, full of anger and wrath.” For there will be none to stand by, none to rescue, nowhere the face of Christ, so mild and calm. But as those who work in the mines are delivered over to certain cruel men, and see none of their friends, but those only that are set over them; so will it be then also: or rather not so, but even far more grievous. For here it is possible to go unto the king, and entreat, and free the condemned person: but there, no longer; for He permits it not, but they continue in the scorching torment, and in so great anguish, as it is not possible for words to tell.

Chrysostom explains the need for such eternal punishment elsewhere. For example, in his 15th homily on 1 Timothy, he emphasizes the value of fear in constraining sin:

Since the greater part are virtuous from constraint rather than from choice, the principle of fear is of great advantage to them in eradicating their desires. Let us therefore listen to the threatenings of hell fire, that we may be benefited by the wholesome fear of it.

And ultimately, the existence of such punishments is a sign of God's regard for human dignity (in comparison to animals), and of the responsibility men have for their deeds:

For, say, if He did not call us to account, would human life then have endured? Should we not then have fallen into the state of beasts? [...]

In the case of men then, it is a mark of goodness to punish, and of cruelty not to punish, and is it not so in the case of God? So that because He is good, therefore He has prepared a hell. [...]

The men before the flood, if they had feared the threat, would not have experienced the execution of it. And we, if we fear the threat, shall not expose ourselves to experience the reality. God forbid we should. (Third homily on Philemon)

Daley writes that Chrysostom "often shows a self-consciously anti-Origenist bias" (108) and clearly rejects tenets of that system, like the "the notion that God's punishment is always medicinal" and that "demons have hope of redemption." He also makes it clear that repentance is not possible after death:

As long as we are here we have good hope, but when we come there, we no longer have it in our power to repent nor to cleanse ourselves from our sins. (Second discourse on Lazarus and the Rich man, 3)

So like Basil, Chrysostom argues against universalism on scriptural and prudential grounds. He sees scripture teaching eternal hell and sees the benefit the doctrine has in scaring sinners away from their sins.

What about Pelagius?

Pelagius, the founder of Pelagianism, was a theologian whose system of thought emphasized the free will of man: he strongly opposed the doctrine of original sin, and claimed that perfection in this life was possible for followers of God.

This system was opposed by the likes of Augustine and Jerome, among others, and many of his beliefs were condemned in AD 418 at the Council of Carthage. However, none of the condemned views relate specifically to the question of eternal suffering in hell. And in more recent times, several books have been written on the thought of Pelagius, based on his own writings (not just those of his opponents).

Two such books (both entitled Pelagius), by Robert Evans and John Ferguson, devote significant space to explaining many details of his thought regarding salvation, sin, and grace, but do not cover his views on hell or judgment.

Based on this evidence, it seems likely, but not certain, that Pelagius did hold to the doctrine of eternal torment, or that at least he did not address it.

Thus we might conjecture that Pelagius developed his views on the free will of man while operating on the premise that evildoers would be subjected to eternal suffering in hell. This seems plausible, as an uncorrupted free will would both allow individual men to avoid hell (if they so choose) and would protect God from the charge of unilaterally sending sinners to hell. But it is difficult to explicitly demonstrated that this is Pelagius's rationale.

More difficulty arises in that scholarship on Pelagius has tended to show that Pelagius may not have held to what Augustine accused him of. Thus, it is far too difficult to really say if Pelagius actually developed a theological rational for his (probable) belief in an eternal hell.

Summary

So here we see two church fathers, and perhaps a third early church writer, who believed in the eternality of hell, and who did not base their views on those of Augustine. Basil and Chrysostom see the doctrine of hell as clearly biblical, and reject the spiritual interpretations of Origen that weaken the threat of hell. However, in Basil and Chrysostom there is no systemic, theological explanation for their eschatology as is present in the writings of Augustine and Origen. Therefore, it is likely that if a non-Augustian theology existed in the early Church which explicitly defended the notion of an eternal hell, we can only know of it by speculating.