Christians once had a social ethic based on love. Aquinas' account of the virtues in his Summa Theologica lays out the full range or moral and theological virtues. In laying those out, he gives special place to justice and to charity.
Justice is in one sense a general virtue that covers all relations between people. The closest thing to rights language in Aquinas is probably legal justice (although conflating them would be a mistake). Note what he says about legal justice:
"...legal justice is said to be a general virtue, in as much, to wit, as it directs the acts of the other virtues to its own end, and this is to move all the other virtues by its command; for just as charity may be called a general virtue in so far as it directs the acts of all the virtues to the Divine good, so too is legal justice, in so far as it directs the acts of all the virtues to the common good. Accordingly, just as charity which regards the Divine good as its proper object, is a special virtue in respect of its essence, so too legal justice is a special virtue in respect of its essence, in so far as it regards the common good as its proper object. And thus it is in the sovereign principally and by way of a mastercraft, while it is secondarily and administratively in his subjects.
However the name of legal justice can be given to every virtue, in so far as every virtue is directed to the common good by the aforesaid legal justice, which though special essentially is nevertheless virtually general. Speaking in this way, legal justice is essentially the same as all virtue, but differs therefrom logically: and it is in this sense that the Philosopher speaks." (ST. II-II. 58)
It is in this sense that human rights language can be somewhat helpful in that it can help direct people toward common good.
But, also note what Aquinas says later about charity:
"Ambrose [Lombard, Sent. iii, D, 23 says that charity is the form of the virtues.
I answer that, In morals the form of an act is taken chiefly from the end. The reason of this is that the principal of moral acts is the will, whose object and form, so to speak, are the end. Now the form of an act always follows from a form of the agent. Consequently, in morals, that which gives an act its order to the end, must needs give the act its form. Now it is evident, in accordance with what has been said (7), that it is charity which directs the acts of all other virtues to the last end, and which, consequently, also gives the form to all other acts of virtue: and it is precisely in this sense that charity is called the form of the virtues, for these are called virtues in relation to "informed" acts." (ST. II-II. 23)
Charity is the form of all the virtues. According to Aquinas, Christians grow into the virtues - all of the virtues - as the Holy Spirit infuses the theological virtue of charity into us. Love makes all the other virtues possible and actual in our lives. From this perspective, there is no dichotomy between love and justice. Love make justice happen. The only argument against a human rights approach is that the reverse is either less likely or perhaps not possible. Justice does not make love happen. The counter to that claim would be that justice creates an environment where love can grow. That is an interesting possibility but it is not the Christian way. Love is infused in us as we are filled with the Holy Spirit that Jesus promised his followers. We are people empowered to love and that enables us to excel in all the virtues, many of which can be generalized and called justice. This is the Christian social ethic and it has nothing to do with Stoicism. Quite the opposite. (Okay, I'll stop, Niebuhr bashing is too easy.)
We might want to converse with the world with human rights language but we have to understand that in doing so we are not using our native language and what we really mean, what we are really about, is Spirit-infused-charity expressed in virtues. And we have to clear that the world lacks the power to sustain human rights and justice because it is still the world and the only power to do such things comes from God and comes in the form of love (apart from the Spirit some degree of moral virtue, including justice is possible, but imperfectly and temporarily). So we have to decide how much energy we want to give to making the world incrementally better and how much we want to give to being the church and thus showing the world that it is the world and powerless to be otherwise.
(Re: Locke/modern expressions, I think the most common understanding now is a Rawlsian, bureaucratic understanding of rights. Michael Sandel gives the most lucid explanations: http://www.justiceharvard.org/)