Using an Orientation Constraint on both eyes so that they are controlled by a helper object.
 

Step 1
Create your helper object. Which kind to create is a completely personal preference. You can use geometry, splines, or Max's ready made helpers. I prefer the Point helper myself.

Step 2
Go to the Motion panel, expand the Assign Controller menu, select Rotation, and click on the Assign Controller button (the question mark).

Step 3
Select Orientation Constraint from the list.

Step 4
Scroll down the panel and select the Add Orientation Target button, and then select the helper object as the target. The eye might rotate after you select the target, but this is normal. Go to the next step to fix this.

Step 5
Scroll down further and check the Keep Initial Offset box. By the way, if you get into the habit of creating all your objects in the same viewport you won't have to do this step. But I tend to create new objects in whatever viewport I happen to be working in at the time, so I'm glad this check box is available.

Step 6
Now go back to step 2 and repeat for the other eye. Once they're both set up you can animate the helper object and it will then animate both eyes for you. Keep in mind that you can place this object anywhere in the scene, at any size you want.

This technique is pretty straight forward to set up and is very easy to animate with. I like to place the helper so that it's kind of floating over the head, and then link it to the head so that I always know where it is when I'm animating.

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