What you can do is, come to qatar and state on the visa that you are visiting your cousin. Either way you can get the tourist visa upon arrival, so I dont think there would be any questions asked. Other way is to get a business visa, I know a few people who live here for around a year on it. You can live here for 1 month to 3 months on a tourist visa, but not quite sure about it. It would be better if you check out the www.moi.gov.qa website or else you can google too.