Upvote:2
The EEA family permit is for family members citizens of EEA countries other than the UK (except under limited circumstances that do not apply here). Furthermore, "extended family members" only qualify if they are either dependent on the principal or are members of the principal's household.
You therefore do not qualify for an EEA family permit for two reasons. First, because your cousin is a citizen of the UK rather than another EU or EEA country or Switzerland, and second because you are not close enough to qualify as a family member, and your circumstances do not qualify you as an extended family member. You should get a standard visitor visa for this trip.