(Reposted with minor revisions)
I. Plantinga's Reformed Epistemology and His Mature Account of Warranted Belief
Since the 60s, Alvin Plantinga has been arguing that belief in God is "properly basic". That is, like belief in material objects, the past, and other minds, belief in God can be rational in a direct, non-inferential way, wholly apart from propositional evidence and argument. This thesis constitutes the core idea of his version of so-called "Reformed Epistemology".
Plantinga's mature defense of his thesis is grounded in a proper functionalist version of epistemic externalism. Plantinga summarizes his account as follows:
"Put in a nutshell, then, a belief has warrant for a person S only if that belief is produced by cognitive faculties [e.g., perception, memory, introspection, reason, and testimony -EA] functioning properly (subject to no dysfunction) in a cognitive environment that is appropriate for S's kind of cognitive faculties, according to a design plan that is successfully aimed at truth."
So that's what's required for a belief to have any warrant at all on Plantinga's account. But he allows that warrant admits of degrees, and he ties the degree of warrant a belief enjoys to the degree of firmness with which it is believed: "We must add, furthermore, that when a belief meets these conditions and does enjoy warrant, the degree of warrant it enjoys depends on the strength of the belief, the firmness with which S holds it." Thus, for such a belief to have a degree of warrant sufficient for knowledge, it must be held with a very high degree of firmness.
Putting these points together, Plantinga's account can be summed up as follows:
I. Conditions of warrant are not met = no warrant (whether the belief is held firmly or not)
II. Conditions of warrant are met + low degree of firmness = low degree of warrant.
III. Conditions of warrant are met + high degree of firmness = high degree of warrant.
So that's Plantinga's account of warranted belief in a nutshell. But how does this account connect to his account of warranted theistic belief in particular?
II. Plantinga's Mature Account of Warranted Theistic Belief: The A/C Model
Plantinga argues that it's epistemically possible (consistent with what we know or reasonably believe) that God has designed us in such a way that we are naturally endowed with a cognitive faculty -- what he (following John Calvin) calls the sensus divinitatis -- that, when functioning properly in an epistemically congenial environment, spontaneously and reliably produces true beliefs about God. So, for example, when one looks at the starry heavens, the sensus divinitatis is (when functioning properly) naturally disposed to spontaneously trigger the belief, "God made all this"; when doing something wrong, it's disposed to trigger the belief, "God disapproves of what I've done"; etc. Therefore, if such belief meets all of the conditions of warrant -- viz., (a) it's produced by a properly functioning cognitive faculty (viz., the sensus divinitatis), (b) the faculty is successfully aimed at truth, and (c) the environment in which such beliefs are formed is epistemically congenial --, Plantinga's account entails that such belief enjoys at least some measure of warrant. And if (d) such belief is held with a very high degree of firmness, the degree of warrant it enjoys is sufficient to constitute knowledge (assuming the belief isn't subject to undefeated defeaters).
We've now looked at Plantinga's account of warranted belief in general and his account of warranted theistic belief in particular. It is now time to take a look at his account of warranted Christian belief.
III. Plantinga's Mature Account of Warranted Christian Belief: The Extended A/C Model
Very roughly, on Plantinga’s model of warranted Christian belief, the Holy Spirit acts on the believer by repairing the sensus divinitatis from the ravages of sin, so that it naturally, spontaneously, and reliably produces true belief about God in the basic (i.e., non-inferential) way. It also repairs the person's affective equipment, so that it is no longer hostile to God and his purposes, but is rather attracted to them and delights in them. Finally, the Holy Spirit functions as an analogue to a properly functioning cognitive faculty by acting directly on the "heart" of a person to produce belief in the core truths of Christianity (what Plantinga calls the Great Things of the Gospel) when they are presented to them (if the person wills to accept the gospel message). Therefore, as with warranted theistic belief as described in Plantinga's A/C model, if Christian belief formed in the way described in his Extended A/C model meets all the conditions of warrant, i.e., (a) it's produced by properly functioning cognitive faculties, (b) the faculties are successfullly aimed at truth, and (c) the environment in which they're formed is epistemically congenial, then it enjoys at least some measure of warrant. And if (d) (due to the internal instigation of the Holy Spirit) the belief is held with a very high degree of firmness, the degree of warrant it enjoys is sufficient to constitute knowledge (again, assuming the belief isn't subject to undefeated defeaters).
We've now seen a sketch of Plantinga's account of warranted belief in general, warranted theistic belief, and warranted Christian belief. What to make of these accounts? I mention eight criticisms below from the literature that have real bite (for more elaboration, click on the links).
IV. Criticisms of Plantinga's Account of Warranted Belief that Have Real Bite
With respect to his accounts of warranted theistic and Christian belief: (i) His analysis of warranted Christian belief can't adequately account for the variability of belief among Christians; (ii) his postulation of a sensus divinitatis in human beings is at odds with the empirical evidence regarding the demographics of theistic belief; and (ironically) (iii) his account entails that the belief of most Christians has little by way of warrant. And of course there's (iv) the Great Pumpkin Objection. But deeper problems lie with his basic account of warrant (see below).
With respect to his account of warranted belief in general: (i) His case for a theistic version of proper functionalism is undercut; indeed, (ii) his theistic version of proper function entails that no beliefs have warrant; (iii) his proper functionalist amendment to straight reliabilism is unmotivated; and (iv) his account of warrant is subject to counterexamples with respect to both to the necessity and sufficiency of the conditions he proposes.
For these reasons, Plantinga's proper functionalism fails to show that Christian or theistic belief can be warranted in the basic or non-inferential way, or even how beliefs can be warranted in general.
 Warranted Christian Belief, p. 156.
 (Plantinga calls his account of warranted theistic belief The A/C Model, inspired as it is by the writings of Aquinas and Calvin.) The following is a rough summary of some key points in ch. 6 of Warranted Christian Belief.
 Question: If all human beings are endowed with a sensus divinitatis, then why do very many people fail to form theistic belief -- at least in the basic, non-inferential way Plantinga describes? Answer: The sensus divinitatis has been damaged by the Fall of Man and human sin. More on this in the next section.
 The following is a very rough summary of some key points in chs. 7-9 of Warranted Christian Belief.
 This part is a bit tricky. For, again, according to the model, the Holy Spirit doesn't produce warranted Christian belief via the cognitive faculty of the sensus divinitatis. Rather, it produces it by acting directly on the "heart" of the person. Therefore, strictly speaking, specifically Christian belief isn't produced by a reliable cognitive faculty, but rather by a reliable process. As you might have guessed, people have raised concerns about this. See, for example, Craig and Moreland's Philosophical Foundations for a Christian Worldview (IVP, 2003), pp. 168-169; Beilby, James. Epistemology as Theology: An Evaluation of Alvin Plantinga's Religious Epistemology (Ashgate, 2005), pp.151-153.
 Cf. Beilby, Epistemology as Theology, pp. 153-156.
 Cf. Maitzen, Stephen. "Divine Hiddenness and the Demographics of Theism" (Religious Studies 42 (2006), pp. 177-191.
 See, for example, Beilby. "Plantinga's Model of Warranted Christian Belief", in Peter-Baker, Deane. Alvin Plantinga (Cambridge University Press, 2007), p. 146; DeRose, Keith."Are Christian Beliefs Properly Basic?" APA Eastern talk, 1998. Available here; Chignell, Andrew. "Epistemology for Saints: Alvin Plantinga's Magnum Opus", Books & Culture (March/April 2002), p. 21.
 Cf. Wunder, Tyler. "Anti-Naturalism and Proper Function”, Religious Studies 44 (2008), pp. 209-224 (notes); Bardon, Adrian. “Reliabilism, Proper Function, and Serendipitous Malfunction”, Philosophical Investigations 30:1 (Jan. 2007), pp. 47-64 (notes); Graham, Peter. "Intelligent Design and Selective History: Two Sources of Purpose and Plan" (in Jonathan Kvanvig, ed. Oxford Studies in Philosophy of Religion, Volume 3, 2011). (A link to the paper can be found here)
 In addition to my formulation of the objection at the link above, see R. Douglass Geivett and Greg Jesson. "Plantinga's Externalism and the Terminus of Warrant-Based Epistemology", Philosophia Christi 3:2, pp. 329-340.
 Feldman, Richard. “Proper Functionalism”, Nous 27 (1993), pp. 34-50.
 See, for example, Greco, J. 2003. “Virtue and Luck, Epistemic and Otherwise,” Metaphilosophy 34:3, 353-6; Lehrer, Keith. "Proper Function vs. Systematic Coherence", in Kvanvig, Jonathan. Warrant in Contemporary Epistemology: Essays in Honor of Plantinga's Theory of Knowledge (Rowman & Littlefield, 1996), pp. 25-46, esp. pp. 32-33; Feldman, “Proper Functionalism”, pp. 34-50; Senor, Thomas. “A Critical Review of Alvin Plantinga’s Warranted Christian Belief”, International Philosophical Quarterly 42:3, Issue 167 (September 2002), 395-396.