score:2
You are an EU national living in the UK and want to sponsor your cousin for a short visit. Your cousin is an Indian national who is working in Oman.
From Paragraph 24 of the rules, your cousin will need an entry clearance. In order to be successful, he will need to clear all of the points listed in Paragraph 41 of the rules. See https://www.gov.uk/government/collections/immigration-rules
Your cousin should apply on-line as a GENERAL VISITOR. Near the end of the application, he will answer some questions about making a biometrics appointment at a facility in Oman. Once the appointment is booked, he will see a page of information on what to do next.
If you are lawfully in the UK and have the financial capacity along with an acceptable level of credibility, you can participate in the application process by offering to help. Because cousins do not have the degree of relationship needed to qualify as family, your cousin will be treated as a FRIEND, and they will need a pretty clear understanding of why you want to do this. For example, do you normally sponsor your cousins in the same way? What's special about this particular point in time?
With this background information, your cousin should start by opening an account and going through the application rigmarole at http://www.vfsglobal.co.uk/oman/