I'm not sure what that means, since beauty is merely a judgment- but it seems entirely possible that science could come to predict, for instance, what a given person will consider beautiful on a given instance, simply from understanding the cognitive processes which underlie our aesthetic judgments.
While accurate, your statement is irrelevant to my argument. Science can amass a body of data on what people consider beautiful, and can make predictions based on that data. Science cannot develop a theory of beauty. Of course, to some extent that is because "beauty" is not "real" in the sense that color, or mass, or material are real. (I do not hold to the Platonic concept of forms.) But to a larger extent, it is because beauty cannot be weighed on a scale, or measured by a gauge.
Well, that's supposing that there is such a thing as being right/wrong above and beyond being considered right/wrong- I see no reason to accept such a presupposition. In any case, supposing there is such a thing as "objective" right or wrong, I still see no reason why science could not, in principle, study or classify it.
It is precisely because there is no such thing as "objective" right and wrong that science cannot study it.
Well, it isn't the best example since science generally doesn't tell us anything about single isolated events, but patterns or regularities;
Incorrect: science can extrapolate from individual data points to patterns, or can interpolate from general patterns to specific instances. In science, there IS no such thing as a "single isolated event." All natural phenomena can be connected to other natural phenomena.
but if miracles did indeed occur, it is conceivable that science could figure out how they work, such that it could predict future cases.
Unlikely. Again, presuming that a miracle occurred, you are dealing with an entity (or entities) with intelligence and volition. How do you persuade such an entity to submit to examination? If God exists, can you weigh him on a scale?
There is a difference between methodological naturalism and metaphysical naturalism. Science relies on the first, not the second.