Clients can make you an admin to their Facebook business page with just a few steps.
With the Facebook business page open, click on Settings on the lefthand side of the screen under the Manage Page section
Scroll down the Page Settings on the left side of your screen and click Page Roles
Where it says "Assign New Page Role" type in the name or email of the person you want to add. (You may need to send them a friend request first if they don't appear in the list to select)
Make sure to select Admin as the role.
Click Add