Are there any well-known Christian nihilists? I have been studying Nietzsche, and I find his ideas thought-provoking. Doing a wider search of the literature on the subject of nihilism, I note that very nearly all of the content that espouses nihilism is irreligious, and all of the religious sources attempt to refute nihilism.

There must be some dissenters in this regard -- it's a big world, and there are many forms of nihilism. Ecclesiastes, for instance, sure sounds nihilist.


  “Meaningless! Meaningless!”
  says the Teacher. “Utterly meaningless!
  Everything is meaningless.”


Usually, I hear this explained away (e.g. -- "Yes, meaningless without God!"), and that may be the correct response, but surely there must be someone with an interpretation of Ecclesiastes that takes Solomon's words at face value.

Are there any well-known Christian nihilists whose literature I can examine? Where can I find discussions on this topic that do not take an anti-nihilist view?

Just to clarify, I am not asking someone to explain whether or why Christianity and nihilism are (in)compatible. I'm trying to get a sense of what's out there on pro-nihilism Christianity.
Yes, there is school of theological nihilism influenced by Nietzsche, known as the "Death of God" movement. Probably the most famous individual associated with it is Paul Tillich. This work explores the idea that the traditional concept of God has "died", and the extent to which faith (or reason, or ethics, etc.) can still exist in such a world. We can argue about whether this sort of thing is nihilist, or existentialist, or both, or not really either; but in any case it comes out of that general area of thought.

It should be distinguished from the older and more "respectable" pursuit of apophatic theology. This is an approach to God founded on describing God in "negative" terms (he is not evil, he is not limited, etc.). Typically, this theology is mystical rather than rational, and Eastern rather than Western. A standard idea in apophatic theology is that God does not exist, meaning that the mode of his "existence" transcends the way in which ordinary everyday stuff is said to "exist". Contemplation of paradoxes associated with the divine is also part of apophatic practice - without necessarily trying to solve them in the manner of rationalist theology. Apophatic theology has influenced nihilistic theology but they are not identical. 

Another relevant writer is Kierkegaard for his exploration of paradox and despair in a Christian context. He is not a nihilist but there is a good deal of later work which responds to him. I would suggest Fear and Trembling as a good starting point (because out of the two books I've read by him, it was the one I liked the best). In it, he works through the story of the Binding of Isaac with an emphasis on the supposed moral of the story, Abraham's greatness through faith; this is contrasted with the anxiety and subjectivity of Abraham's personal experience, in the context of an apparently immoral command to murder his son.