from the cic website...http://www.cic.gc.ca/english/immigrate/sponsor/relatives-apply-who.asp
(your cousin) can sponsor:
parents
grandparents
brothers or sisters, nephews or nieces, granddaughters or grandsons who are orphaned, under 18 years of age and not married or in a common-law relationship
another relative of any age or relationship but only under specific conditions (see Note below)
accompanying relatives of the above (for example, spouse, partner and dependent children).
Note: you can sponsor one relative regardless of age or relationship only if you do not have a living spouse or common-law partner, conjugal partner, a son or daughter, parent, grandparent, sibling, uncle, aunt, nephew or niece who could be sponsored as a member of the family class, and you do not have any relative who is a Canadian citizen or a permanent resident or registered as an Indian under the Indian Act.
Who cannot be sponsored
Other relatives, such as brothers and sisters over 18, or adult independent children cannot be sponsored. However, if they apply to immigrate under the Skilled Worker Class, they may get extra points for adaptability for having a relative in Canada.