I'm not that expert in this line. but what i did when i failed to obtain a residence visa for my wife, i arranged visit visa ( 'jiara shakhsi' in arabic) and I was the sponsor for her visa. within 1 week of her arrival i extended it for further 5 months. I don't know if you can sponsor your cousin for such a visit. Better consult the typist shop people. one typing shop/agency is located behind Habib qatar exchange at national area.
best of luck.