Suppose that some event X occurs which cannot be explained by naturalism. Moreover, suppose X occurs repeatedly and is well-documented, but at the same time, is not repeatable (via laboratories, etc.). An example of this might be the stigmata, the apparently inexplicable appearance of Jesus' crucifixion wounds.
1. If a genuine occurrence cannot be explained by natural processes, it is either supernatural or inexplicable. (Premise)
2. The stigmata is a genuine occurrence that cannot be explained by natural processes. (Premise)
3. Hence, the stigmata is either supernatural or inexplicable. (From 1 and 2)
4. Genuine occurrences are not inexplicable. (Premise, PSR)
5. Therefore, the stigmata is supernatural. (From 1, 2, and 4)
I'm sure that there will be no trouble in accepting (1), (3), and to a slightly lesser extent (4). (4) assumes that events really have explanations, and do not just occur without any reason whatsoever. For someone who already accepts a fairly benign version of the PSR, that leaves us with (2).
The stigmata is a well-documented phenomena.  Naturalistic explanations range from deliberate hoax to psychosomatic self-infliction. Regardless of where one stands on this issue, I think it deserves more attention and study.
 See the following links: http://www.newadvent.org/cathen/14294b.htm, http://www.springerlink.com/content/mr77672706625313/