I believe that AirPort Utility offers a feature to change permissions for drives. But it does involve setting up disk accounts.
1. Open AirPort Utility (Please make sure you are running v6 of AirPort Utility.)
2. Select the Time Capsule.
3. If necessary, enter the device's password in to AirPort Utility and press "Enter Password".
4. Press "Edit".
5. Select the "Disks" tab.
6. Where it states "Secure Shared Disks:" select from the pop-up menu "With accounts"
7. Click the + button.
8. Choose a Account Name, a Account Password and verify the password by typing it again.
9. Where it states "File Sharing Access:", select the option that best suites you. Press "Save" when done.
10. Repeat from Step 7 to create any more users.
11. When completed, press the Update button below, and follow the onscreen instructions.
This is the best I can find. Hope it helps.