+1(514) 937-9445 or Toll-free (Canada & US) +1 (888) 947-9445
Your cousin can only sponsor his/her spouse, parents or children.
 
There is the "lonely Canadian" option. But it doesn't cover cousins.

See: http://www.cic.gc.ca/english/immigrate/sponsor/relatives-apply-who.asp "Who you can sponsor" Option 2.