According to this link, you are not able to sponsor your cousin to come to the UK on a Visit/Family Visa
https://www.gov.uk/family-visit-visa/eligibility
Your family in the UK
You must be able to show that you’re visiting one of the following family members in the UK:
- spouse or civil partner
- children
- parents or siblings
- grandparents or grandchildren
- your spouse’s or civil partner’s siblings or parents
- your child’s spouse or civil partner
- step parents, step children or step siblings
- a person you’ve been living with in a long-term relationship, as if you were married or in a civil partnership, for at least 2 years before the day you apply
Your family member must also be one of the following:
- a British citizen
- settled in the UK
- granted asylum in the UK
- under humanitarian protection in the UK