Here is another fallacious argument skeptics will have heard:
There are ways of knowing other than the scientific one
The scientific method is not the only source of truth
..or similar wording. It is an appeal to other ways of knowing apart from science. The claim is that the tools of critical thinking and science are not sufficient to evaluate the believer’s claim; therefore the believer's claim has validity despite the lack of evidence for it.
The flaw in the argument
No one is claiming that science has all the answers or is always right. However, science has proved to be the most reliable method we know for evaluating claims and figuring out how the universe works. If the believer is claiming that there is a better method, it is up to him or her to justify that claim. To demonstrate this, believers need to explain their better method for evaluating claims, and provide evidence that it is indeed a better method. If they cannot do this their appeal to other ways of knowing is vacuous and fallacious.
For examples of this fallacy in action, you can do no worse that go to the astrologers such as Robert Hand or Dorian Gieseler Greenbaum. Of course, they have no choice but to utilize this fallacy since all rational evidence shows that astrology is made-up and astrology doesn’t work. Astrologers aren’t the only ones though. For some other examples you could read some of the believer comments posted to this blog. A prime example is this plea for the truth of reincarnation.