It will be extremely difficult to make an argument supporting the existence of paranormal phenomena in general, as there is no scientific evidence for their existence. In fact, many claims of paranormal expertise, such as those of psychics, astrologers, and mediums, can be a cover for fraud. There are a few possible ways that you might make a legitimate and convincing argument:
First, you might choose one specific practice such as astrology or ESP and make the argument that these are ways in which people with high emotional intelligence can offer what are basically counseling services. One does not need to believe that planetary positions affect personalities or events to accept that some individuals, despite a lack of professional training in psychology, might be good life coaches who use astrology or palmistry as a framework for acting as life coaches or counselors.
Another possibility might be to choose one specific prescientific culture and argue that the evidence for what we now would call paranormal events was actually quite convincing within the framework of that specific culture. For example, one might look at shamanistic practices, voodoo, or other forms of ancestor worship and examine why people would have believed in such things and how they functioned socially.
To argue for the existence of some paranormal phenomenon such as ESP or communication with the dead, it would be a good idea to focus on one very narrow topic where the research might be somewhat equivocal. This would need to cite empirical studies conducted in controlled circumstances and published in peer-reviewed journals. Rather than making a positive claim, which most educated readers would disbelieve, a better technique would be to open up a space for argument by making a very modest claim such as this: "Although most claims of ESP have been disproven, a limited number of studies show statistical variations which might suggest that under certain circumstances, limited forms of communication using poorly understood modalities might be evident." This could be followed by an argument that such studies are worth additional investigation.