To expand slightly on what Conifold mentioned, according to IEP the "modest foundationalism" has Alvin Platinga as a prime exponent; Wikipedia mostly covers that under "reformed epistemology" although it does say under "modest foundationalism" that:
Reformed epistemology is a form of modest foundationalism which takes religious beliefs as basic because they are non-inferentially justified: their justification arises from religious experience, rather than prior beliefs.
And in the more focused wiki article:
In Plantinga's view, warrant is defined as the property of beliefs that makes them knowledge. Plantinga argues that a properly basic belief in God is warranted when produced by a sound mind, in an environment supportive of proper thought in accord with a design plan successfully aimed at truth. Because there is an epistemically possible model according to which theistic belief is properly basic and designed to form true belief in God, belief in God is probably warranted if theism is true. Plantinga does not argue that this model is true, but only that if it is true, theistic belief is also likely true, because then theistic belief would result from our belief-forming faculties functioning as they were designed. [...]
Other prominent defenders of Reformed epistemology include William Lane Craig, William Alston, and Michael C. Rea.
(I think Nicholas Wolterstorff can be safely added to that list.) From Plantinga Wikipedia bio:
Ultimately, Plantinga argues that epistemological naturalism- i.e. epistemology that holds that warrant is dependent on natural faculties—is best supported by supernaturalist metaphysics—in this case, the belief in a creator God or designer who has laid out a design plan that includes cognitive faculties conducive to attaining knowledge. [...]
William Lane Craig wrote in his work Reasonable Faith that he considers Plantinga to be the greatest Christian philosopher alive.
According to Wikipedia's bio of Platinga he "was the 30th most-cited contemporary author in the Stanford Encyclopedia of Philosophy" according to one analysis. (N.B.: William Alston was #48 in that list. Robert Audi (see below) #114; Nicholas Wolterstorff #152.)
Although Platinga may be most famous now, according to IEP:
William Alston probably did the most to rehabilitate foundationalism.
You can probably find more related figures in the list of presidents of the Society of Christian Philosophers.
Robert Audi who is on that list also subscribes to some weakened version:
Audi has defended a position he calls "fallibilistic foundationalism." He thinks that the foundationalist response is the only tenable option of the epistemic regress argument. This states that if every belief has to be justified by some other, then the only options are four: infinite regress, circularity, stopping at a belief that isn't knowledge, and stopping at a basic belief that is itself justified. If the only alternative is the fourth, then if one has knowledge, one has foundational knowledge. Audi considers that foundationalism is usually taken to be infallible. That is, it is normally associated with the view that knowledge is founded on basic beliefs that are axiomatic and necessarily true, and that the rest of knowledge is deduced from this set of beliefs. Audi thinks that foundationalism may be fallible, in the sense that the suprastructure of beliefs may be derived inductively from the basic beliefs, and hence may be fallible. He also thinks that basic beliefs need not be necessary truths, but merely have some structure which makes epistemic transition possible. For example, the belief that one is in the presence of an object arises causally from visual perception.
I'm not sure where Robert Merrihew Adams stood on that as his wiki bio is a bit undeveloped (he's #37 in the SEP mention ranks though.)
The "weak foundationalism" of BonJour gets a honorable mention of sorts on IEP but mostly a subject of criticism from another modest foundationalist--Van Cleve. (Amusingly enough BonJour and Van Cleve "tied" on SEP at #179.)
IEP also mentions that reliabilism might fall under the broad tent of foundationalism:
reliabilism makes plausible a form of structural foundationalism which stops the regress of justification
Wikipedia [also] classifies reliabilism an externalist foundationalist account:
Reliabilism is an externalist foundationalist theory, initially proposed by Alvin Goldman, which argues that a belief is justified if it is reliably produced, meaning that it will be probably true. Goldman distinguished between two kinds of justification for beliefs: belief-dependent and belief-independent. A belief-dependent process uses prior beliefs to produce new beliefs; a belief-independent process does not, using other stimuli instead. Beliefs produced this way are justified because the processes that cause them are reliable; this might be because we have evolved to reach good conclusions when presented with sense-data, meaning the conclusions we draw from our senses are usually true.
And a number of SCP notables like Linda Zagzebski although declaratively responsibilists have argued closer to reliabilists:
Some virtue responsibilists have adopted an approach similar to that of virtue reliabilists by giving virtue concepts a crucial role in an analysis of knowledge or justification. Linda Zagzebski, for instance, claims that knowledge is belief arising from what she calls “acts of intellectual virtue” (1996).
(I don't understand this bit too well, but it seems to be some kind of argument that virtue is foundational or some such.)
I'll also note that SEP (unlike IEP and Wikipedia) uses the term "modest foundationalism" with a fairly different meaning, denoting some other efforts, not seemingly related to Christian philosophers:
Some contemporary epistemologists seek a more modest foundationalism that will make it much easier to respond to the skeptic’s arguments. Michael Huemer’s (2001) phenomenal conservatism and Jim Pryor’s (2000) dogmatism are both views that are far more “permissive” in allowing a far more extensive range of beliefs to have foundational justification. And their views are not unrelated to Chisholm’s longstanding efforts (e.g., 1989) to locate noninferential justification for believing various propositions about one’s past and physical environment in the character of one’s experiential states.
But otherwise (agreeing with Wikipedia on this) it also classifies reliabilism as an externalist foundationalist viewpoint...
While the externalist defends radically different views than those of classical foundationalists, the structure of knowledge and justification that emerges from such theories is still often a foundationalist structure. We might first illustrate the point by examining the view defended by the most prominent of the externalists, Alvin Goldman’s reliabilism. [...]
[However...] On most externalist accounts of noninferentially justified belief there are literally no a priori constraints on what might end up being noninferentially justified.
[And among the criticisms listed] Reliabilism seems to yield the wrong result, justifying too many beliefs.
Although Plantinga is very cited on SEP, (amusingly) he isn't cited on that page, but some other works quickly point out that Plantinga also resorts to a form of reliabilism but that he bases his on a warrant (from God basically).
Comparing reliabilism with the theory of warrant, Nicla Vassallo claims that “the difference between proper functionalism and reliabilism is slight, since the cognitive faculties that function properly are usually reliable and since, even from a reliabilist point of view, the cognitive processes considered are those that bring to truth” (Vassallo 1999, p. 131). [...] She sustains that with appropriate modification – essentially renouncing to the concept of proper function – Plantinga’s theory of warrant would be “compressed in Goldman’s sophisticated reliabilism”. [...]
Plantinga chooses Goldman’s reliabilism as the paradigmatic theory that is, in his words, “clearly compatible with the existence of God” (Plantinga 1996, p. 356). [...But] In order to accept Goldmanian reliabilism, Plantinga needs to take it to a higher level of reliability, for once in a Cartesian fashion, as only the Christian God can offer such level of warrant.