Solution 1:

You can do this using Parental Controls on the Guest account. See Apple's KB article regarding this for the procedure:

  • OS X Mountain Lion: Filter inappropriate Internet content

Manage a user with parental controls

  1. Choose Apple menu > System Preferences, and then click Parental Controls.

  2. Click the lock if it’s not unlocked, and enter an administrator name and password.

  3. Select a user in the list of users, and then click Web.

  4. In the Website Restrictions section, select the Internet restrictions you want for Safari.

    • To allow Safari to access Internet content without filtering, select “Allow unrestricted access to websites.”

    • To filter inappropriate Internet content or websites, select “Try to limit access to adult websites automatically.”

      To allow or restrict specific sites, click Customize.

    • To limit access to only specific websites, select “Allow access to only these websites.”

      To add a website to the list, click Add (+) below the list, choose Add Bookmark from the pop-up menu, enter a bookmark name and webpage address, and then click OK.

      To add a bookmark folder, click Add (+) below the list, choose Add Folder, and then type a name for the folder.

      To remove a bookmark or bookmark folder from the list, select it and click Delete (-) below the list.

But to fully protect the computer from potential harm from Internet regardless of account used one has to block any downloads and installations without explicit approval. (I do that to protect my self from my self :)

Each browser has they own set of tools that can be used to protect user and computer. Loots of good add-on's in Firefox.

As an example for Firefox you would use a add-on ..Block downloads,

lock down bookmarks/addons/downloads with a password.

Solution 2:

When you use the Guest Account feature, it is isolated from the rest of the system. The guest user has no administrative rights and anything that is saved by the user is deleted after logging out. You can fine tune what the guest user has access to (this is a good article) but AFAIK, and in regard to whether or not your cousin can download something that would be harmful to your computer, the Guest Account is completely safe to use.

According to Apple:

Important: Files created by a guest user are deleted when the user logs out. A temporary home folder is created for the guest user’s files, but this folder and its contents are deleted when the user logs out.

and with even more restriction:

When FileVault is turned on, guest users can only log in and use Safari. Guests can’t access your FileVault-encrypted disk or create files. Instead, they log in and use Safari from your computer’s built-in recovery disk.

Unless your cousin works for the NSA (I say this tongue-in-cheek), I don't think you have anything to worry about if he is using the Guest Account feature.