Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Your parents should not reject your cousin as a husband unless there is a considerable reason. If there no good reason, you should kindly and gently approach them trying to convince them of your viewpoint.
In responding to your question, Dr. Muhammad Salama, PhD, Islamic Studies in English, Associate Professor at the Faculty of Islamic Sciences al-Madinah International University (Mediu), states:
It is really strange that your parents do not want to marry you to your cousin. You did not point out the reason of their objection. Perhaps, they know him to be a bad person or not suitable for you as a husband.
However, if there is no good reason for their objection and you are sure that your cousin is a religious and a God-fearing person, then you need to approach your parents kindly and appeal to their passion toward you and their care for your happiness. You may seek the help of other members of the family to convince them of this marriage.
Above all, you need to pray sincerely and seriously to Allah Almighty to help you. You need to pray istikharah (Prayer where one asks Allah to choose for him/her) and ask Allah Almighty to choose what is best for you.
Come closer to Allah and He will guide you. Let Allah, not your passion, lead your life.
Allah Almighty knows best.