So you do not have a spouse, common-law partner, conjugal partner (boyfriend/girlfriend), children, mother, father, brothers, sisters, nieces, nephews, grandparents or aunts or uncles living. Basically, your cousin's parents are not living as well and you have NO living relatives in the world other than these cousins.
If that is the case, then yes, you can sponsor them as a member of the family class assuming you meet the elgibility requirements and they are not medically or criminally inadmissible.