Maybe it's just as well because I think the topic title is slightly misconceived.
A concept is incoherent when it contains mutually contradictory features. For example the concepts of a married bachelor, or a giant pygmy, or a round square are incoherent because the first term in each contradicts and precludes the second and vice-versa.
But naturalism itself is not incoherent in this way. There don't appear, to me at least, any internal contradictions in the view that nature, as can be described by science, is all there is.
However, this is not to say that there are not coherence problems in trying to live as a consistent naturalist. Many who adopt a naturalist worldview find themselves unable to live with it.
For example, most of us desire a number of what might be called existential qualities in our lives, none of which can be sustained under naturalism:
- We desire meaning in our lives. Viktor Frankl, a holocaust survivor, wrote in Man's Search for Meaning that men can't live without meaning. Yet on naturalism, there is no meaning to be found anywhere in the cosmos, just "blind, pitiless indifference" in the words of Richard Dawkins.
- We desire to ground our moral judgments in something solid, but on naturalism morality is "just an illusion, fobbed off on us by our genes, to get us to cooperate with each other" according to Michael Ruse. Nothing is really right or wrong in a moral sense. It's just useful or not in promoting the survival of the species.
- We desire justice, but on naturalism death is the end and the selfish and cruel have the same fate as their victims - extinction. Unless there's accountability for our actions justice is a fiction.
- We desire dignity, but on naturalism we're just animals, gobs of protoplasm in thrall to our genes, with no free will and no real specialness. In the words of Stephen Hawking "The human race is just a chemical scum on a moderate-sized planet." Supreme Court Justice Oliver Wendell Holmes puts it this way: "I see no reason for attributing to man a significance different in kind from that which belongs to a baboon or a grain of sand." On naturalism no lives matter.
- We desire to live, but on naturalism we all die and when those we love are gone they're gone forever. The late Will Provine of Cornell University writes: "There are no gods, no purposes, and no goal-directed forces of any kind. There is no life after death...no ultimate foundation for ethics, no ultimate meaning in life, and no free will."
- We desire happiness, but on naturalism the fate of most humans who've ever walked the earth has been simply to be born, suffer, and die. There are moments of pleasure, Woody Allen once said, "but they don't add up to anything."
There's an incoherence in naturalism, to be sure, but it's not found in the concept. Rather, it's found in the attempt to live as though the concept were true.